समीकरण (2y=10x+14) को (y=mx+c) रूप में लिखने पर ढाल क्या होगी?
When the equation (2y=10x+14) is written in (y=mx+c) form, what will be the slope?
#slope
#rearrange_equation
#linear_form
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A (3)
B (5)
C (7)
D (10)
Explanation opens after your attempt
Step 1
Concept
Dividing by (2) gives (y=5x+7). Therefore the slope is (5).
Step 2
Why this answer is correct
The correct answer is B. (5). Dividing by (2) gives (y=5x+7). Therefore the slope is (5).
Step 3
Exam Tip
(2) से भाग देने पर (y=5x+7) मिलता है। इसलिए ढाल (5) है।
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समीकरण (4y=12x-20) का (y)-अवरोध क्या है?
What is the (y)-intercept of the equation (4y=12x-20)?
#y_intercept
#rearrange_equation
#constant_term
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A (3)
B (-5)
C (12)
D (-20)
Explanation opens after your attempt
Step 1
Concept
Dividing by (4) gives (y=3x-5). The constant term (-5) is the (y)-intercept.
Step 2
Why this answer is correct
The correct answer is B. (-5). Dividing by (4) gives (y=3x-5). The constant term (-5) is the (y)-intercept.
Step 3
Exam Tip
(4) से भाग देने पर (y=3x-5) मिलता है। स्थिर पद (-5) (y)-अवरोध है।
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समीकरण (3x+y=11) की ढाल क्या है?
What is the slope of the equation (3x+y=11)?
#standard_form
#slope
#rearrange
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A (3)
B (11)
C (-3)
D (-11)
Explanation opens after your attempt
Step 1
Concept
It is written as (y=-3x+11). The coefficient of (x), (-3), is the slope.
Step 2
Why this answer is correct
The correct answer is C. (-3). It is written as (y=-3x+11). The coefficient of (x), (-3), is the slope.
Step 3
Exam Tip
इसे (y=-3x+11) लिखा जाता है। (x) का गुणांक (-3) ढाल है।
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समीकरण (5x-y=15) का (y)-अवरोध क्या है?
What is the (y)-intercept of the equation (5x-y=15)?
#standard_form
#y_intercept
#sign_change
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A (-15)
B (5)
C (-5)
D (15)
Explanation opens after your attempt
Step 1
Concept
From (5x-y=15), we get (y=5x-15). Therefore the (y)-intercept is (-15).
Step 2
Why this answer is correct
The correct answer is A. (-15). From (5x-y=15), we get (y=5x-15). Therefore the (y)-intercept is (-15).
Step 3
Exam Tip
(5x-y=15) से (y=5x-15) मिलता है। इसलिए (y)-अवरोध (-15) है।
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रेखा (y=18-6x) की ढाल और (y)-अवरोध कौन से हैं?
What are the slope and (y)-intercept of the line (y=18-6x)?
#slope
#y_intercept
#rearranged_form
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A ढाल (-6) और (y)-अवरोध (18) / Slope (-6) and (y)-intercept (18)
B ढाल (18) और (y)-अवरोध (-6) / Slope (18) and (y)-intercept (-6)
C ढाल (6) और (y)-अवरोध (18) / Slope (6) and (y)-intercept (18)
D ढाल (-18) और (y)-अवरोध (6) / Slope (-18) and (y)-intercept (6)
Explanation opens after your attempt
Correct Answer
A. ढाल (-6) और (y)-अवरोध (18) / Slope (-6) and (y)-intercept (18)
Step 1
Concept
Write it as (y=-6x+18). So the slope is (-6) and the (y)-intercept is (18).
Step 2
Why this answer is correct
The correct answer is A. ढाल (-6) और (y)-अवरोध (18) / Slope (-6) and (y)-intercept (18). Write it as (y=-6x+18). So the slope is (-6) and the (y)-intercept is (18).
Step 3
Exam Tip
इसे (y=-6x+18) लिखें। इसलिए ढाल (-6) और (y)-अवरोध (18) है।
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रेखा (y=-4x+13) (y)-अक्ष को किस बिंदु पर काटती है?
At which point does the line (y=-4x+13) cut the (y)-axis?
#y_intercept
#point_on_axis
#graph
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A ( (13,0) )
B ( (0,-4) )
C ( (0,13) )
D ( (-4,13) )
Explanation opens after your attempt
Correct Answer
C. ( (0,13) )
Step 1
Concept
On the (y)-axis, (x=0). Then (y=13).
Step 2
Why this answer is correct
The correct answer is C. ( (0,13) ). On the (y)-axis, (x=0). Then (y=13).
Step 3
Exam Tip
(y)-अक्ष पर (x=0) होता है। तब (y=13) मिलता है।
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यदि रेखा की ढाल (7) और (y)-अवरोध (-2) है तो समीकरण कौन सा होगा?
If a line has slope (7) and (y)-intercept (-2), which equation is correct?
#equation_from_slope_intercept
#model_selection
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A (y=7x-2)
B (y=-2x+7)
C (y=7x+2)
D (y=-7x-2)
Explanation opens after your attempt
Correct Answer
A. (y=7x-2)
Step 1
Concept
In (y=mx+c), put (m=7) and (c=-2). The correct equation is (y=7x-2).
Step 2
Why this answer is correct
The correct answer is A. (y=7x-2). In (y=mx+c), put (m=7) and (c=-2). The correct equation is (y=7x-2).
Step 3
Exam Tip
रूप (y=mx+c) में (m=7) और (c=-2) रखें। सही समीकरण (y=7x-2) है।
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यदि रेखा की ढाल (-8) और (y)-अवरोध (5) है तो समीकरण कौन सा होगा?
If a line has slope (-8) and (y)-intercept (5), which equation is correct?
#negative_slope
#equation_selection
#intercept
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A (y=8x+5)
B (y=5x-8)
C (y=-8x+5)
D (y=-5x+8)
Explanation opens after your attempt
Correct Answer
C. (y=-8x+5)
Step 1
Concept
The slope is the coefficient of (x) and the (y)-intercept is the constant term. So (y=-8x+5) is correct.
Step 2
Why this answer is correct
The correct answer is C. (y=-8x+5). The slope is the coefficient of (x) and the (y)-intercept is the constant term. So (y=-8x+5) is correct.
Step 3
Exam Tip
ढाल (x) का गुणांक और (y)-अवरोध स्थिर पद होता है। इसलिए (y=-8x+5) सही है।
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रेखा (y=mx-6) की ढाल (4) है। (m) का मान क्या है?
The line (y=mx-6) has slope (4). What is the value of (m)?
#parameter_slope
#linear_form
#slope
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A (4)
B (-4)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
In (y=mx+c), (m) itself is the slope. Therefore (m=4).
Step 2
Why this answer is correct
The correct answer is A. (4). In (y=mx+c), (m) itself is the slope. Therefore (m=4).
Step 3
Exam Tip
(y=mx+c) में (m) ही ढाल है। इसलिए (m=4) है।
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रेखा (y=-3x+c) (y)-अक्ष को ( (0,9) ) पर काटती है। (c) क्या है?
The line (y=-3x+c) cuts the (y)-axis at ( (0,9) ). What is (c)?
#parameter_intercept
#y_axis
#constant_term
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A (-3)
B (3)
C (9)
D (-9)
Explanation opens after your attempt
Step 1
Concept
On the (y)-axis, (x=0), and (y=c). Therefore (c=9).
Step 2
Why this answer is correct
The correct answer is C. (9). On the (y)-axis, (x=0), and (y=c). Therefore (c=9).
Step 3
Exam Tip
(y)-अक्ष पर (x=0) होता है और (y=c) होता है। इसलिए (c=9) है।
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रेखा (y=5x+1) में (x) के (4) बढ़ने पर (y) कितना बढ़ेगा?
In the line (y=5x+1), how much will (y) increase when (x) increases by (4)?
#rate_of_change
#total_change
#slope
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A (9)
B (20)
C (5)
D (4)
Explanation opens after your attempt
Step 1
Concept
The slope is (5). An increase of (4) in (x) makes (y) increase by \(5\times4=20\).
Step 2
Why this answer is correct
The correct answer is B. (20). The slope is (5). An increase of (4) in (x) makes (y) increase by \(5\times4=20\).
Step 3
Exam Tip
ढाल (5) है। (x) में (4) की वृद्धि से (y) \(5\times4=20\) बढ़ेगा।
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रेखा (y=-6x+20) में (x) के (3) बढ़ने पर (y) में क्या परिवर्तन होगा?
In the line (y=-6x+20), what change will occur in (y) when (x) increases by (3)?
#negative_slope
#rate_of_change
#total_change
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A (18) बढ़ेगा / Increases by (18)
B (20) घटेगा / Decreases by (20)
C (18) घटेगा / Decreases by (18)
D (3) घटेगा / Decreases by (3)
Explanation opens after your attempt
Correct Answer
C. (18) घटेगा / Decreases by (18)
Step 1
Concept
The slope is (-6). The change is \(-6\times3=-18\), so (y) decreases by (18).
Step 2
Why this answer is correct
The correct answer is C. (18) घटेगा / Decreases by (18). The slope is (-6). The change is \(-6\times3=-18\), so (y) decreases by (18).
Step 3
Exam Tip
ढाल (-6) है। परिवर्तन \(-6\times3=-18\) है इसलिए (y) (18) घटेगा।
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समीकरण (6y=-12x+30) में ढाल और (y)-अवरोध क्या हैं?
What are the slope and (y)-intercept in the equation (6y=-12x+30)?
#rearrange_equation
#slope
#y_intercept
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A ढाल (-12) और (y)-अवरोध (30) / Slope (-12) and (y)-intercept (30)
B ढाल (-2) और (y)-अवरोध (5) / Slope (-2) and (y)-intercept (5)
C ढाल (2) और (y)-अवरोध (-5) / Slope (2) and (y)-intercept (-5)
D ढाल (6) और (y)-अवरोध (30) / Slope (6) and (y)-intercept (30)
Explanation opens after your attempt
Correct Answer
B. ढाल (-2) और (y)-अवरोध (5) / Slope (-2) and (y)-intercept (5)
Step 1
Concept
Dividing by (6) gives (y=-2x+5). So the slope is (-2) and the (y)-intercept is (5).
Step 2
Why this answer is correct
The correct answer is B. ढाल (-2) और (y)-अवरोध (5) / Slope (-2) and (y)-intercept (5). Dividing by (6) gives (y=-2x+5). So the slope is (-2) and the (y)-intercept is (5).
Step 3
Exam Tip
(6) से भाग देने पर (y=-2x+5) मिलता है। इसलिए ढाल (-2) और (y)-अवरोध (5) है।
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समीकरण (2x+3y=12) का (y)-अवरोध क्या है?
What is the (y)-intercept of the equation (2x+3y=12)?
#standard_form
#y_intercept
#substitution
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A (2)
B (3)
C (4)
D (12)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) gives (3y=12) and (y=4). Therefore the (y)-intercept is (4).
Step 2
Why this answer is correct
The correct answer is C. (4). Putting (x=0) gives (3y=12) and (y=4). Therefore the (y)-intercept is (4).
Step 3
Exam Tip
(x=0) रखने पर (3y=12) और (y=4) मिलता है। इसलिए (y)-अवरोध (4) है।
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समीकरण (4x+2y=10) की ढाल क्या है?
What is the slope of the equation (4x+2y=10)?
#standard_form
#slope
#rearrange
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A (2)
B (-2)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
(2y=-4x+10) and (y=-2x+5). Therefore the slope is (-2).
Step 2
Why this answer is correct
The correct answer is B. (-2). (2y=-4x+10) and (y=-2x+5). Therefore the slope is (-2).
Step 3
Exam Tip
(2y=-4x+10) और (y=-2x+5) है। इसलिए ढाल (-2) है।
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रेखा \(y=\frac{5}{2}x-7\) में (x) के (2) बढ़ने पर (y) कितना बढ़ेगा?
In the line \(y=\frac{5}{2}x-7\), how much will (y) increase when (x) increases by (2)?
#fraction_slope
#total_change
#rate_of_change
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A (2)
B (5)
C (7)
D (10)
Explanation opens after your attempt
Step 1
Concept
The slope is \(\frac{5}{2}\). The change will be \(\frac{5}{2}\times2=5\).
Step 2
Why this answer is correct
The correct answer is B. (5). The slope is \(\frac{5}{2}\). The change will be \(\frac{5}{2}\times2=5\).
Step 3
Exam Tip
ढाल \(\frac{5}{2}\) है। परिवर्तन \(\frac{5}{2}\times2=5\) होगा।
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रेखा \(y=-\frac{3}{4}x+6\) में (x) के (8) बढ़ने पर (y) कितना घटेगा?
In the line \(y=-\frac{3}{4}x+6\), how much will (y) decrease when (x) increases by (8)?
#fraction_slope
#negative_slope
#total_change
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A (3)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
The slope is \(-\frac{3}{4}\). The change is \(-\frac{3}{4}\times8=-6\), so the decrease is (6).
Step 2
Why this answer is correct
The correct answer is C. (6). The slope is \(-\frac{3}{4}\). The change is \(-\frac{3}{4}\times8=-6\), so the decrease is (6).
Step 3
Exam Tip
ढाल \(-\frac{3}{4}\) है। परिवर्तन \(-\frac{3}{4}\times8=-6\) है इसलिए कमी (6) है।
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यदि (y=mx+2) रेखा ( (3,17) ) से गुजरती है तो (m) क्या होगा?
If (y=mx+2) passes through ( (3,17) ), what will (m) be?
#find_slope
#point_given
#parameter
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Substituting the point gives (17=3m+2). Thus (3m=15) and (m=5).
Step 2
Why this answer is correct
The correct answer is C. (5). Substituting the point gives (17=3m+2). Thus (3m=15) and (m=5).
Step 3
Exam Tip
बिंदु रखने पर (17=3m+2) मिलता है। इससे (3m=15) और (m=5) है।
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यदि (y=-2x+c) रेखा ( (4,1) ) से गुजरती है तो (c) क्या होगा?
If (y=-2x+c) passes through ( (4,1) ), what will (c) be?
#find_intercept
#point_given
#parameter
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
Substituting the point gives (1=-2(4)+c). Therefore (c=9).
Step 2
Why this answer is correct
The correct answer is C. (9). Substituting the point gives (1=-2(4)+c). Therefore (c=9).
Step 3
Exam Tip
बिंदु रखने पर (1=-2(4)+c) मिलता है। इसलिए (c=9) है।
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यदि रेखा की ढाल (2) है और वह (y)-अक्ष को ( (0,-5) ) पर काटती है तो समीकरण क्या होगा?
If a line has slope (2) and cuts the (y)-axis at ( (0,-5) ), what is its equation?
#equation_from_slope_intercept
#negative_intercept
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A (y=2x-5)
B (y=-5x+2)
C (y=2x+5)
D (y=-2x-5)
Explanation opens after your attempt
Correct Answer
A. (y=2x-5)
Step 1
Concept
The slope is (2) and the (y)-intercept is (-5). Therefore (y=2x-5).
Step 2
Why this answer is correct
The correct answer is A. (y=2x-5). The slope is (2) and the (y)-intercept is (-5). Therefore (y=2x-5).
Step 3
Exam Tip
ढाल (2) है और (y)-अवरोध (-5) है। इसलिए (y=2x-5) है।
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यदि रेखा की ढाल (-5) है और (x=0) पर (y=3) है तो रेखा कौन सी है?
If a line has slope (-5) and (y=3) at (x=0), which line is it?
#equation_selection
#negative_slope
#intercept
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A (y=5x+3)
B (y=-5x+3)
C (y=-3x+5)
D (y=-5x-3)
Explanation opens after your attempt
Correct Answer
B. (y=-5x+3)
Step 1
Concept
(y=3) at (x=0) means the (y)-intercept is (3). With slope (-5), the line is (y=-5x+3).
Step 2
Why this answer is correct
The correct answer is B. (y=-5x+3). (y=3) at (x=0) means the (y)-intercept is (3). With slope (-5), the line is (y=-5x+3).
Step 3
Exam Tip
(x=0) पर (y=3) का अर्थ (y)-अवरोध (3) है। ढाल (-5) से (y=-5x+3) बनता है।
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रेखाएं (y=4x+7) और (y=4x-2) के बारे में सही कथन क्या है?
Which statement about the lines (y=4x+7) and (y=4x-2) is correct?
#compare_slopes
#parallel_lines
#coefficient
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A दोनों की ढाल समान है / Both have the same slope
B दोनों का (y)-अवरोध समान है / Both have the same (y)-intercept
C दोनों की ढाल (0) है / Both slopes are (0)
D दोनों मूल से गुजरती हैं / Both pass through origin
Explanation opens after your attempt
Correct Answer
A. दोनों की ढाल समान है / Both have the same slope
Step 1
Concept
Both have coefficient (4) of (x). Therefore both have the same slope.
Step 2
Why this answer is correct
The correct answer is A. दोनों की ढाल समान है / Both have the same slope. Both have coefficient (4) of (x). Therefore both have the same slope.
Step 3
Exam Tip
दोनों में (x) का गुणांक (4) है। इसलिए दोनों की ढाल समान है।
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रेखाएं (y=6x-1) और (y=-3x-1) के बारे में सही कथन क्या है?
Which statement about the lines (y=6x-1) and (y=-3x-1) is correct?
#compare_intercepts
#constant_term
#linear_graph
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A दोनों की ढाल समान है / Both have the same slope
B दोनों का (y)-अवरोध समान है / Both have the same (y)-intercept
C दोनों क्षैतिज हैं / Both are horizontal
D दोनों की ढाल धनात्मक है / Both slopes are positive
Explanation opens after your attempt
Correct Answer
B. दोनों का (y)-अवरोध समान है / Both have the same (y)-intercept
Step 1
Concept
Both have constant term (-1). Therefore both have the same (y)-intercept.
Step 2
Why this answer is correct
The correct answer is B. दोनों का (y)-अवरोध समान है / Both have the same (y)-intercept. Both have constant term (-1). Therefore both have the same (y)-intercept.
Step 3
Exam Tip
दोनों में स्थिर पद (-1) है। इसलिए दोनों का (y)-अवरोध समान है।
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कौन सी रेखा ढाल (0) और (y)-अवरोध (-4) रखती है?
Which line has slope (0) and (y)-intercept (-4)?
#zero_slope
#negative_intercept
#equation_selection
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A (y=-4x)
B (y=0x-4)
C (y=4x-4)
D (y=x-4)
Explanation opens after your attempt
Correct Answer
B. (y=0x-4)
Step 1
Concept
With slope (0), the coefficient of (x) is (0). With (y)-intercept (-4), the line is (y=0x-4).
Step 2
Why this answer is correct
The correct answer is B. (y=0x-4). With slope (0), the coefficient of (x) is (0). With (y)-intercept (-4), the line is (y=0x-4).
Step 3
Exam Tip
ढाल (0) होने पर (x) का गुणांक (0) होगा। (y)-अवरोध (-4) से (y=0x-4) है।
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कौन सी रेखा मूल बिंदु से गुजरती है और ढाल (9) रखती है?
Which line passes through the origin and has slope (9)?
#origin
#slope
#equation_selection
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A (y=9x)
B (y=x+9)
C (y=9x+1)
D (y=-9x)
Explanation opens after your attempt
Step 1
Concept
Passing through the origin means the (y)-intercept is (0). With slope (9), (y=9x) is correct.
Step 2
Why this answer is correct
The correct answer is A. (y=9x). Passing through the origin means the (y)-intercept is (0). With slope (9), (y=9x) is correct.
Step 3
Exam Tip
मूल बिंदु से गुजरने पर (y)-अवरोध (0) होता है। ढाल (9) होने से (y=9x) सही है।
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रेखा (y=-x+8) में (x=0) पर (y) का मान क्या है?
What is the value of (y) at (x=0) in the line (y=-x+8)?
#value_at_zero
#y_intercept
#substitution
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A (8)
B (-1)
C (0)
D (-8)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) gives (y=8). This is the (y)-intercept.
Step 2
Why this answer is correct
The correct answer is A. (8). Putting (x=0) gives (y=8). This is the (y)-intercept.
Step 3
Exam Tip
(x=0) रखने पर (y=8) मिलता है। यही (y)-अवरोध है।
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रेखा (y=14-7x) में (x=0) पर (y) का मान क्या है?
What is the value of (y) at (x=0) in the line (y=14-7x)?
#value_at_zero
#y_intercept
#rearranged_form
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A (7)
B (-7)
C (14)
D (-14)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0), (y=14). Therefore the (y)-intercept is (14).
Step 2
Why this answer is correct
The correct answer is C. (14). Putting (x=0), (y=14). Therefore the (y)-intercept is (14).
Step 3
Exam Tip
(x=0) रखने पर (y=14) होता है। इसलिए (y)-अवरोध (14) है।
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यदि (y=mx+c) में (m<0) और (c<0) है तो कौन सा कथन सही है?
If (m<0) and (c<0) in (y=mx+c), which statement is correct?
#sign_of_slope
#sign_of_intercept
#concept
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A ढाल धनात्मक और (y)-अवरोध ऋणात्मक है / Slope is positive and (y)-intercept is negative
B ढाल ऋणात्मक और (y)-अवरोध ऋणात्मक है / Slope is negative and (y)-intercept is negative
C ढाल शून्य और (y)-अवरोध धनात्मक है / Slope is zero and (y)-intercept is positive
D दोनों धनात्मक हैं / Both are positive
Explanation opens after your attempt
Correct Answer
B. ढाल ऋणात्मक और (y)-अवरोध ऋणात्मक है / Slope is negative and (y)-intercept is negative
Step 1
Concept
(m) is the slope and (c) is the (y)-intercept. Since both are negative, statement (B) is correct.
Step 2
Why this answer is correct
The correct answer is B. ढाल ऋणात्मक और (y)-अवरोध ऋणात्मक है / Slope is negative and (y)-intercept is negative. (m) is the slope and (c) is the (y)-intercept. Since both are negative, statement (B) is correct.
Step 3
Exam Tip
(m) ढाल है और (c) (y)-अवरोध है। दोनों ऋणात्मक होने से कथन (B) सही है।
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यदि (y=mx+c) में (m>0) और (c=0) है तो रेखा के बारे में क्या सही है?
If (m>0) and (c=0) in (y=mx+c), what is correct about the line?
#positive_slope
#origin
#graph_behavior
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A रेखा घटती है और मूल से नहीं गुजरती / The line decreases and does not pass through origin
B रेखा बढ़ती है और मूल बिंदु से गुजरती है / The line increases and passes through origin
C रेखा क्षैतिज है / The line is horizontal
D रेखा का (y)-अवरोध ऋणात्मक है / The (y)-intercept is negative
Explanation opens after your attempt
Correct Answer
B. रेखा बढ़ती है और मूल बिंदु से गुजरती है / The line increases and passes through origin
Step 1
Concept
(m>0) makes the line increasing and (c=0) makes it pass through the origin. Read the signs carefully.
Step 2
Why this answer is correct
The correct answer is B. रेखा बढ़ती है और मूल बिंदु से गुजरती है / The line increases and passes through origin. (m>0) makes the line increasing and (c=0) makes it pass through the origin. Read the signs carefully.
Step 3
Exam Tip
(m>0) से रेखा बढ़ती है और (c=0) से वह मूल बिंदु से गुजरती है। संकेतों को ध्यान से पढ़ें।
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समीकरण (y+4=3x) का (y)-अवरोध क्या है?
What is the (y)-intercept of the equation (y+4=3x)?
#rearrange_equation
#y_intercept
#constant_term
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A (3)
B (4)
C (-4)
D (-3)
Explanation opens after your attempt
Step 1
Concept
It is written as (y=3x-4). The constant term (-4) is the (y)-intercept.
Step 2
Why this answer is correct
The correct answer is C. (-4). It is written as (y=3x-4). The constant term (-4) is the (y)-intercept.
Step 3
Exam Tip
इसे (y=3x-4) लिखा जाता है। स्थिर पद (-4) (y)-अवरोध है।
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समीकरण (y-5=-2x) की ढाल क्या है?
What is the slope of the equation (y-5=-2x)?
#rearrange_equation
#slope
#coefficient
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A (5)
B (-2)
C (2)
D (-5)
Explanation opens after your attempt
Step 1
Concept
Write it as (y=-2x+5). The coefficient of (x) is (-2).
Step 2
Why this answer is correct
The correct answer is B. (-2). Write it as (y=-2x+5). The coefficient of (x) is (-2).
Step 3
Exam Tip
इसे (y=-2x+5) लिखें। (x) का गुणांक (-2) है।
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रेखा (y=ax-3) की ढाल (-6) है। समीकरण कौन सा होगा?
The line (y=ax-3) has slope (-6). Which equation is correct?
#parameter_slope
#equation_selection
#negative_slope
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A (y=6x-3)
B (y=-6x-3)
C (y=-3x-6)
D (y=3x-6)
Explanation opens after your attempt
Correct Answer
B. (y=-6x-3)
Step 1
Concept
The slope equals (a). Putting (a=-6) gives (y=-6x-3).
Step 2
Why this answer is correct
The correct answer is B. (y=-6x-3). The slope equals (a). Putting (a=-6) gives (y=-6x-3).
Step 3
Exam Tip
ढाल (a) के बराबर है। (a=-6) रखने पर (y=-6x-3) मिलता है।
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रेखा (y=4x+b) का (y)-अवरोध (11) है। समीकरण कौन सा होगा?
The line (y=4x+b) has (y)-intercept (11). Which equation is correct?
#parameter_intercept
#equation_selection
#linear_form
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A (y=11x+4)
B (y=4x-11)
C (y=4x+11)
D (y=-4x+11)
Explanation opens after your attempt
Correct Answer
C. (y=4x+11)
Step 1
Concept
(b) is the (y)-intercept. Putting (b=11) gives (y=4x+11).
Step 2
Why this answer is correct
The correct answer is C. (y=4x+11). (b) is the (y)-intercept. Putting (b=11) gives (y=4x+11).
Step 3
Exam Tip
(b) (y)-अवरोध है। (b=11) रखने पर (y=4x+11) बनता है।
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दो रेखाएं (y=-3x+4) और (y=-3x-8) कैसी हैं?
How are the two lines (y=-3x+4) and (y=-3x-8) related?
#compare_slopes
#parallel_lines
#negative_slope
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A उनकी ढाल समान है / Their slopes are the same
B उनके (y)-अवरोध समान हैं / Their (y)-intercepts are the same
C दोनों की ढाल (0) है / Both slopes are (0)
D दोनों मूल से गुजरती हैं / Both pass through the origin
Explanation opens after your attempt
Correct Answer
A. उनकी ढाल समान है / Their slopes are the same
Step 1
Concept
Both have coefficient (-3) of (x). Their constant terms are different, so their (y)-intercepts are different.
Step 2
Why this answer is correct
The correct answer is A. उनकी ढाल समान है / Their slopes are the same. Both have coefficient (-3) of (x). Their constant terms are different, so their (y)-intercepts are different.
Step 3
Exam Tip
दोनों में (x) का गुणांक (-3) है। स्थिर पद अलग हैं इसलिए (y)-अवरोध अलग होंगे।
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दो रेखाएं (y=2x-6) और (y=-7x-6) कैसी समानता रखती हैं?
What similarity do the two lines (y=2x-6) and (y=-7x-6) have?
#compare_intercepts
#constant_term
#linear_graph
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A दोनों की ढाल समान है / Both have the same slope
B दोनों का (y)-अवरोध समान है / Both have the same (y)-intercept
C दोनों क्षैतिज हैं / Both are horizontal
D दोनों बढ़ती हुई हैं / Both are increasing
Explanation opens after your attempt
Correct Answer
B. दोनों का (y)-अवरोध समान है / Both have the same (y)-intercept
Step 1
Concept
Both have constant term (-6). Therefore both have the same (y)-intercept.
Step 2
Why this answer is correct
The correct answer is B. दोनों का (y)-अवरोध समान है / Both have the same (y)-intercept. Both have constant term (-6). Therefore both have the same (y)-intercept.
Step 3
Exam Tip
दोनों में स्थिर पद (-6) है। इसलिए दोनों का (y)-अवरोध समान है।
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रेखा (y=-15) की ढाल और (y)-अवरोध क्या हैं?
What are the slope and (y)-intercept of the line (y=-15)?
#zero_slope
#horizontal_line
#negative_intercept
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A ढाल (-15) और (y)-अवरोध (0) / Slope (-15) and (y)-intercept (0)
B ढाल (0) और (y)-अवरोध (-15) / Slope (0) and (y)-intercept (-15)
C ढाल (1) और (y)-अवरोध (-15) / Slope (1) and (y)-intercept (-15)
D ढाल (0) और (y)-अवरोध (15) / Slope (0) and (y)-intercept (15)
Explanation opens after your attempt
Correct Answer
B. ढाल (0) और (y)-अवरोध (-15) / Slope (0) and (y)-intercept (-15)
Step 1
Concept
(y=-15) is a horizontal line. Its slope is (0) and its (y)-intercept is (-15).
Step 2
Why this answer is correct
The correct answer is B. ढाल (0) और (y)-अवरोध (-15) / Slope (0) and (y)-intercept (-15). (y=-15) is a horizontal line. Its slope is (0) and its (y)-intercept is (-15).
Step 3
Exam Tip
(y=-15) क्षैतिज रेखा है। इसकी ढाल (0) और (y)-अवरोध (-15) है।
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रेखा (y=0x+6) में (x) के (10) बढ़ने पर (y) में कितना परिवर्तन होगा?
In the line (y=0x+6), what change will occur in (y) when (x) increases by (10)?
#zero_slope
#rate_of_change
#horizontal_line
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A (0)
B (6)
C (10)
D (60)
Explanation opens after your attempt
Step 1
Concept
The slope is (0). So even when (x) changes, there is no change in (y).
Step 2
Why this answer is correct
The correct answer is A. (0). The slope is (0). So even when (x) changes, there is no change in (y).
Step 3
Exam Tip
ढाल (0) है। इसलिए (x) बदलने पर भी (y) में कोई परिवर्तन नहीं होगा।
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रेखा \(y=\frac{2}{3}x+1\) में (x) के (9) बढ़ने पर (y) कितना बढ़ेगा?
In the line \(y=\frac{2}{3}x+1\), how much will (y) increase when (x) increases by (9)?
#fraction_slope
#rate_of_change
#total_change
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A (3)
B (6)
C (9)
D (12)
Explanation opens after your attempt
Step 1
Concept
The slope is \(\frac{2}{3}\). The change will be \(\frac{2}{3}\times9=6\).
Step 2
Why this answer is correct
The correct answer is B. (6). The slope is \(\frac{2}{3}\). The change will be \(\frac{2}{3}\times9=6\).
Step 3
Exam Tip
ढाल \(\frac{2}{3}\) है। परिवर्तन \(\frac{2}{3}\times9=6\) होगा।
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रेखा \(y=-\frac{4}{5}x+12\) में (x) के (15) बढ़ने पर (y) कितना घटेगा?
In the line \(y=-\frac{4}{5}x+12\), how much will (y) decrease when (x) increases by (15)?
#fraction_slope
#negative_slope
#change
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A (8)
B (10)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
The slope is \(-\frac{4}{5}\). The change is \(-\frac{4}{5}\times15=-12\), so the decrease is (12).
Step 2
Why this answer is correct
The correct answer is C. (12). The slope is \(-\frac{4}{5}\). The change is \(-\frac{4}{5}\times15=-12\), so the decrease is (12).
Step 3
Exam Tip
ढाल \(-\frac{4}{5}\) है। परिवर्तन \(-\frac{4}{5}\times15=-12\) है इसलिए कमी (12) है।
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यदि (y=mx-4) रेखा ( (2,6) ) से गुजरती है तो ढाल क्या है?
If the line (y=mx-4) passes through ( (2,6) ), what is the slope?
#find_slope
#point_given
#parameter
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Substituting the point gives (6=2m-4). Thus (2m=10) and (m=5).
Step 2
Why this answer is correct
The correct answer is C. (5). Substituting the point gives (6=2m-4). Thus (2m=10) and (m=5).
Step 3
Exam Tip
बिंदु रखने पर (6=2m-4) मिलता है। इससे (2m=10) और (m=5) है।
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यदि (y=5x+c) रेखा ( (3,8) ) से गुजरती है तो (y)-अवरोध क्या है?
If the line (y=5x+c) passes through ( (3,8) ), what is the (y)-intercept?
#find_intercept
#point_given
#linear_form
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A (7)
B (-7)
C (23)
D (-23)
Explanation opens after your attempt
Step 1
Concept
Substituting the point gives (8=5(3)+c). Therefore (c=-7) is the (y)-intercept.
Step 2
Why this answer is correct
The correct answer is B. (-7). Substituting the point gives (8=5(3)+c). Therefore (c=-7) is the (y)-intercept.
Step 3
Exam Tip
बिंदु रखने पर (8=5(3)+c) मिलता है। इसलिए (c=-7) (y)-अवरोध है।
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कौन सी रेखा (x=0) पर (y=12) देती है और ढाल (-4) रखती है?
Which line gives (y=12) at (x=0) and has slope (-4)?
#equation_selection
#negative_slope
#intercept
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A (y=4x+12)
B (y=-4x+12)
C (y=12x-4)
D (y=-12x+4)
Explanation opens after your attempt
Correct Answer
B. (y=-4x+12)
Step 1
Concept
At (x=0), (y=12) gives (c=12). With slope (-4), (y=-4x+12) is correct.
Step 2
Why this answer is correct
The correct answer is B. (y=-4x+12). At (x=0), (y=12) gives (c=12). With slope (-4), (y=-4x+12) is correct.
Step 3
Exam Tip
(x=0) पर (y=12) से (c=12) मिलता है। ढाल (-4) होने से (y=-4x+12) सही है।
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कौन सी रेखा (x=0) पर (y=-8) देती है और ढाल (6) रखती है?
Which line gives (y=-8) at (x=0) and has slope (6)?
#equation_selection
#positive_slope
#negative_intercept
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A (y=6x-8)
B (y=-8x+6)
C (y=-6x-8)
D (y=6x+8)
Explanation opens after your attempt
Correct Answer
A. (y=6x-8)
Step 1
Concept
(y=-8) at (x=0) means (c=-8). With slope (6), the line is (y=6x-8).
Step 2
Why this answer is correct
The correct answer is A. (y=6x-8). (y=-8) at (x=0) means (c=-8). With slope (6), the line is (y=6x-8).
Step 3
Exam Tip
(x=0) पर (y=-8) का अर्थ (c=-8) है। ढाल (6) से रेखा (y=6x-8) है।
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रेखा (y=9x+2) और (y=-9x+2) के बारे में सही कथन क्या है?
Which statement about (y=9x+2) and (y=-9x+2) is correct?
#compare_slope_intercept
#constant_term
#linear_lines
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A ढाल समान है और (y)-अवरोध अलग हैं / Slopes are same and (y)-intercepts are different
B ढाल अलग है और (y)-अवरोध समान हैं / Slopes are different and (y)-intercepts are same
C दोनों की ढाल (0) है / Both slopes are (0)
D दोनों मूल से गुजरती हैं / Both pass through origin
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Correct Answer
B. ढाल अलग है और (y)-अवरोध समान हैं / Slopes are different and (y)-intercepts are same
Step 1
Concept
The slopes are (9) and (-9), but the constant term (2) is the same. So the (y)-intercepts are the same.
Step 2
Why this answer is correct
The correct answer is B. ढाल अलग है और (y)-अवरोध समान हैं / Slopes are different and (y)-intercepts are same. The slopes are (9) and (-9), but the constant term (2) is the same. So the (y)-intercepts are the same.
Step 3
Exam Tip
ढालें (9) और (-9) हैं लेकिन स्थिर पद (2) समान है। इसलिए (y)-अवरोध समान हैं।
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रेखा (y=-2x+10) और (y=-2x-3) के बारे में सही कथन क्या है?
Which statement about (y=-2x+10) and (y=-2x-3) is correct?
#compare_slope_intercept
#parallel_lines
#negative_slope
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A ढाल समान है और (y)-अवरोध अलग हैं / Slopes are same and (y)-intercepts are different
B ढाल अलग है और (y)-अवरोध समान हैं / Slopes are different and (y)-intercepts are same
C दोनों के (y)-अवरोध (0) हैं / Both (y)-intercepts are (0)
D दोनों की ढाल धनात्मक है / Both slopes are positive
Explanation opens after your attempt
Correct Answer
A. ढाल समान है और (y)-अवरोध अलग हैं / Slopes are same and (y)-intercepts are different
Step 1
Concept
Both have coefficient (-2) of (x). The constant terms (10) and (-3) are different.
Step 2
Why this answer is correct
The correct answer is A. ढाल समान है और (y)-अवरोध अलग हैं / Slopes are same and (y)-intercepts are different. Both have coefficient (-2) of (x). The constant terms (10) and (-3) are different.
Step 3
Exam Tip
दोनों में (x) का गुणांक (-2) है। स्थिर पद (10) और (-3) अलग हैं।
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रेखा (y=11x-4) में ढाल का चिन्ह और (y)-अवरोध का चिन्ह क्या है?
What are the signs of the slope and the (y)-intercept in the line (y=11x-4)?
#sign_analysis
#slope
#intercept
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A ढाल धनात्मक और (y)-अवरोध ऋणात्मक / Slope positive and (y)-intercept negative
B ढाल ऋणात्मक और (y)-अवरोध धनात्मक / Slope negative and (y)-intercept positive
C दोनों धनात्मक / Both positive
D दोनों ऋणात्मक / Both negative
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Correct Answer
A. ढाल धनात्मक और (y)-अवरोध ऋणात्मक / Slope positive and (y)-intercept negative
Step 1
Concept
The slope is (11), which is positive, and the constant term (-4) is negative. Check the signs separately.
Step 2
Why this answer is correct
The correct answer is A. ढाल धनात्मक और (y)-अवरोध ऋणात्मक / Slope positive and (y)-intercept negative. The slope is (11), which is positive, and the constant term (-4) is negative. Check the signs separately.
Step 3
Exam Tip
ढाल (11) है जो धनात्मक है और स्थिर पद (-4) ऋणात्मक है। संकेत अलग-अलग देखें।
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रेखा (y=-7x+9) में ढाल का चिन्ह और (y)-अवरोध का चिन्ह क्या है?
What are the signs of the slope and the (y)-intercept in the line (y=-7x+9)?
#sign_analysis
#negative_slope
#positive_intercept
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A दोनों धनात्मक / Both positive
B ढाल ऋणात्मक और (y)-अवरोध धनात्मक / Slope negative and (y)-intercept positive
C ढाल धनात्मक और (y)-अवरोध ऋणात्मक / Slope positive and (y)-intercept negative
D दोनों शून्य / Both zero
Explanation opens after your attempt
Correct Answer
B. ढाल ऋणात्मक और (y)-अवरोध धनात्मक / Slope negative and (y)-intercept positive
Step 1
Concept
The slope (-7) is negative and the (y)-intercept (9) is positive. Identify the coefficient of (x) and the constant term.
Step 2
Why this answer is correct
The correct answer is B. ढाल ऋणात्मक और (y)-अवरोध धनात्मक / Slope negative and (y)-intercept positive. The slope (-7) is negative and the (y)-intercept (9) is positive. Identify the coefficient of (x) and the constant term.
Step 3
Exam Tip
ढाल (-7) ऋणात्मक है और (y)-अवरोध (9) धनात्मक है। (x) के गुणांक और स्थिर पद को पहचानें।
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यदि (y=3x+c) का (y)-अवरोध (2) है तो (x=4) पर (y) क्या होगा?
If (y=3x+c) has (y)-intercept (2), what will (y) be at (x=4)?
#evaluate_line
#intercept_given
#slope
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A (10)
B (12)
C (14)
D (16)
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Step 1
Concept
The (y)-intercept (2) gives (c=2). Putting (x=4), (y=3(4)+2=14).
Step 2
Why this answer is correct
The correct answer is C. (14). The (y)-intercept (2) gives (c=2). Putting (x=4), (y=3(4)+2=14).
Step 3
Exam Tip
(y)-अवरोध (2) से (c=2) है। (x=4) रखने पर (y=3(4)+2=14) है।
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यदि (y=mx-5) की ढाल (4) है तो (x=3) पर (y) क्या होगा?
If (y=mx-5) has slope (4), what will (y) be at (x=3)?
#evaluate_line
#slope_given
#substitution
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A (5)
B (7)
C (9)
D (12)
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Step 1
Concept
Slope (4) gives (m=4). Putting (x=3), (y=4(3)-5=7).
Step 2
Why this answer is correct
The correct answer is B. (7). Slope (4) gives (m=4). Putting (x=3), (y=4(3)-5=7).
Step 3
Exam Tip
ढाल (4) से (m=4) है। (x=3) रखने पर (y=4(3)-5=7) मिलता है।
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रेखा (y=-5x+16) में (x) (1) से (5) तक बढ़े तो (y) में कुल परिवर्तन क्या होगा?
In the line (y=-5x+16), what is the total change in (y) when (x) increases from (1) to (5)?
#total_change
#negative_slope
#rate_of_change
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A (20) बढ़ेगा / Increases by (20)
B (16) घटेगा / Decreases by (16)
C (20) घटेगा / Decreases by (20)
D (5) घटेगा / Decreases by (5)
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Correct Answer
C. (20) घटेगा / Decreases by (20)
Step 1
Concept
The change in (x) is (5-1=4). The change in (y) is \(-5\times4=-20\).
Step 2
Why this answer is correct
The correct answer is C. (20) घटेगा / Decreases by (20). The change in (x) is (5-1=4). The change in (y) is \(-5\times4=-20\).
Step 3
Exam Tip
(x) में परिवर्तन (5-1=4) है। (y) का परिवर्तन \(-5\times4=-20\) है।
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