समीकरण (9x+3y=24) को (y=mx+c) रूप में लिखने पर ढाल और (y)-अवरोध क्या होंगे?
When (9x+3y=24) is written in (y=mx+c) form, what are the slope and (y)-intercept?
#standard_form
#slope_intercept
#rearrange
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A ढाल (-3), (y)-अवरोध (8) / Slope (-3), (y)-intercept (8)
B ढाल (3), (y)-अवरोध (8) / Slope (3), (y)-intercept (8)
C ढाल (-9), (y)-अवरोध (3) / Slope (-9), (y)-intercept (3)
D ढाल (9), (y)-अवरोध (-3) / Slope (9), (y)-intercept (-3)
Explanation opens after your attempt
Correct Answer
A. ढाल (-3), (y)-अवरोध (8) / Slope (-3), (y)-intercept (8)
Step 1
Concept
From (3y=-9x+24), (y=-3x+8). The coefficient is slope and the constant term is the (y)-intercept.
Step 2
Why this answer is correct
The correct answer is A. ढाल (-3), (y)-अवरोध (8) / Slope (-3), (y)-intercept (8). From (3y=-9x+24), (y=-3x+8). The coefficient is slope and the constant term is the (y)-intercept.
Step 3
Exam Tip
(3y=-9x+24) से (y=-3x+8) मिलता है। गुणांक ढाल और स्थिर पद (y)-अवरोध है।
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समीकरण (4x-8y=32) का (y)-अवरोध क्या है?
What is the (y)-intercept of the equation (4x-8y=32)?
#standard_form
#y_intercept
#substitution
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A (4)
B (-4)
C (8)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) gives (-8y=32) and (y=-4). Therefore the (y)-intercept is (-4).
Step 2
Why this answer is correct
The correct answer is B. (-4). Putting (x=0) gives (-8y=32) and (y=-4). Therefore the (y)-intercept is (-4).
Step 3
Exam Tip
(x=0) रखने पर (-8y=32) और (y=-4) मिलता है। इसलिए (y)-अवरोध (-4) है।
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यदि रेखा (y=(k-5)x+1) की ढाल (12) है, तो (k) क्या है?
If the line (y=(k-5)x+1) has slope (12), what is (k)?
#parameter_slope
#linear_form
#solve
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A (12)
B (5)
C (17)
D (7)
Explanation opens after your attempt
Step 1
Concept
The slope is (k-5). From (k-5=12), (k=17).
Step 2
Why this answer is correct
The correct answer is C. (17). The slope is (k-5). From (k-5=12), (k=17).
Step 3
Exam Tip
ढाल (k-5) है। (k-5=12) से (k=17) मिलता है।
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रेखा (y=-4x+c) बिंदु ( (3,-5) ) से गुजरती है। इसका (y)-अवरोध क्या है?
The line (y=-4x+c) passes through ( (3,-5) ). What is its (y)-intercept?
#find_intercept
#point_given
#negative_slope
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A (5)
B (7)
C (9)
D (11)
Explanation opens after your attempt
Step 1
Concept
Substituting the point gives (-5=-4(3)+c). Therefore (c=7), the (y)-intercept.
Step 2
Why this answer is correct
The correct answer is B. (7). Substituting the point gives (-5=-4(3)+c). Therefore (c=7), the (y)-intercept.
Step 3
Exam Tip
बिंदु रखने पर (-5=-4(3)+c) मिलता है। इसलिए (c=7), जो (y)-अवरोध है।
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रेखा (y=mx+7) बिंदु ( (-2,1) ) से गुजरती है। इसकी ढाल क्या है?
The line (y=mx+7) passes through ( (-2,1) ). What is its slope?
#find_slope
#point_given
#parameter
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A (2)
B (3)
C (-2)
D (-3)
Explanation opens after your attempt
Step 1
Concept
Substituting the point gives (1=-2m+7). Thus (-2m=-6) and (m=3).
Step 2
Why this answer is correct
The correct answer is B. (3). Substituting the point gives (1=-2m+7). Thus (-2m=-6) and (m=3).
Step 3
Exam Tip
बिंदु रखने पर (1=-2m+7) मिलता है। इससे (-2m=-6) और (m=3) है।
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समीकरण (3x+5y=25) की ढाल क्या है?
What is the slope of the equation (3x+5y=25)?
#standard_form
#fraction_slope
#rearrange
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A \(-\frac{3}{5}\)
B \(\frac{3}{5}\)
C (5)
D (25)
Explanation opens after your attempt
Correct Answer
A. \(-\frac{3}{5}\)
Step 1
Concept
From (5y=-3x+25), \(y=-\frac{3}{5}x+5\). Therefore the slope is \(-\frac{3}{5}\).
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{5}\). From (5y=-3x+25), \(y=-\frac{3}{5}x+5\). Therefore the slope is \(-\frac{3}{5}\).
Step 3
Exam Tip
(5y=-3x+25) से \(y=-\frac{3}{5}x+5\) मिलता है। इसलिए ढाल \(-\frac{3}{5}\) है।
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यदि (ay=24x-36) की ढाल (6) है, तो (a) का मान क्या है?
If (ay=24x-36) has slope (6), what is the value of (a)?
#parameter_slope
#rearrange_equation
#hard
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A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
\(y=\frac{24}{a}x-\frac{36}{a}\). From \(\frac{24}{a}=6\), (a=4).
Step 2
Why this answer is correct
The correct answer is B. (4). \(y=\frac{24}{a}x-\frac{36}{a}\). From \(\frac{24}{a}=6\), (a=4).
Step 3
Exam Tip
\(y=\frac{24}{a}x-\frac{36}{a}\) होगा। \(\frac{24}{a}=6\) से (a=4) मिलता है।
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यदि (ky=18x-54) का (y)-अवरोध (-9) है, तो (k) क्या है?
If (ky=18x-54) has (y)-intercept (-9), what is (k)?
#parameter_intercept
#rearrange_equation
#hard
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A (3)
B (4)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(y=\frac{18}{k}x-\frac{54}{k}\). From \(-\frac{54}{k}=-9\), (k=6).
Step 2
Why this answer is correct
The correct answer is C. (6). \(y=\frac{18}{k}x-\frac{54}{k}\). From \(-\frac{54}{k}=-9\), (k=6).
Step 3
Exam Tip
\(y=\frac{18}{k}x-\frac{54}{k}\) होगा। \(-\frac{54}{k}=-9\) से (k=6) मिलता है।
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रेखा (y=(3p-2)x+4) की ढाल (16) है। (p) क्या होगा?
The line (y=(3p-2)x+4) has slope (16). What will (p) be?
#parameter_slope
#linear_polynomial
#solve
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
The slope is (3p-2). From (3p-2=16), (3p=18) and (p=6).
Step 2
Why this answer is correct
The correct answer is C. (6). The slope is (3p-2). From (3p-2=16), (3p=18) and (p=6).
Step 3
Exam Tip
ढाल (3p-2) है। (3p-2=16) से (3p=18) और (p=6) है।
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यदि (y=(r-4)x+(r+6)) मूल बिंदु से गुजरती है, तो इसकी ढाल क्या होगी?
If (y=(r-4)x+(r+6)) passes through the origin, what will be its slope?
#origin
#parameter
#find_slope
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A (-10)
B (-6)
C (2)
D (10)
Explanation opens after your attempt
Step 1
Concept
To pass through the origin, (r+6=0). Thus (r=-6) and the slope is (r-4=-10).
Step 2
Why this answer is correct
The correct answer is A. (-10). To pass through the origin, (r+6=0). Thus (r=-6) and the slope is (r-4=-10).
Step 3
Exam Tip
मूल बिंदु से गुजरने के लिए (r+6=0) होगा। इसलिए (r=-6) और ढाल (r-4=-10) है।
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समीकरण (12x+3y-21=0) में ढाल और (y)-अवरोध क्या हैं?
What are the slope and (y)-intercept in (12x+3y-21=0)?
#general_form
#slope_intercept
#rearrange
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A ढाल (4), (y)-अवरोध (7) / Slope (4), (y)-intercept (7)
B ढाल (-4), (y)-अवरोध (7) / Slope (-4), (y)-intercept (7)
C ढाल (-12), (y)-अवरोध (3) / Slope (-12), (y)-intercept (3)
D ढाल (12), (y)-अवरोध (-3) / Slope (12), (y)-intercept (-3)
Explanation opens after your attempt
Correct Answer
B. ढाल (-4), (y)-अवरोध (7) / Slope (-4), (y)-intercept (7)
Step 1
Concept
From (3y=-12x+21), (y=-4x+7). So the slope is (-4) and the (y)-intercept is (7).
Step 2
Why this answer is correct
The correct answer is B. ढाल (-4), (y)-अवरोध (7) / Slope (-4), (y)-intercept (7). From (3y=-12x+21), (y=-4x+7). So the slope is (-4) and the (y)-intercept is (7).
Step 3
Exam Tip
(3y=-12x+21) से (y=-4x+7) मिलता है। इसलिए ढाल (-4) और (y)-अवरोध (7) है।
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समीकरण (8x-2y+10=0) का (y)-अवरोध क्या है?
What is the (y)-intercept of (8x-2y+10=0)?
#general_form
#y_intercept
#substitution
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A (4)
B (5)
C (-4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) gives (-2y+10=0). Thus (y=5), so the (y)-intercept is (5).
Step 2
Why this answer is correct
The correct answer is B. (5). Putting (x=0) gives (-2y+10=0). Thus (y=5), so the (y)-intercept is (5).
Step 3
Exam Tip
(x=0) रखने पर (-2y+10=0) मिलता है। इससे (y=5), इसलिए (y)-अवरोध (5) है।
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यदि दो रेखाएं (y=(q+3)x-6) और (y=11x+2) समान ढाल रखती हैं, तो (q) क्या है?
If the two lines (y=(q+3)x-6) and (y=11x+2) have the same slope, what is (q)?
#compare_slopes
#parameter
#parallel_lines
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
For equal slopes, (q+3=11). This gives (q=8).
Step 2
Why this answer is correct
The correct answer is D. (8). For equal slopes, (q+3=11). This gives (q=8).
Step 3
Exam Tip
समान ढाल के लिए (q+3=11) होना चाहिए। इससे (q=8) मिलता है।
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यदि (y=-7x+s) और (y=4x-12) का (y)-अवरोध समान है, तो (s) क्या होगा?
If (y=-7x+s) and (y=4x-12) have the same (y)-intercept, what will (s) be?
#compare_intercepts
#parameter
#constant_term
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A (-12)
B (-7)
C (4)
D (12)
Explanation opens after your attempt
Step 1
Concept
The first line has (y)-intercept (s), and the second has (-12). If they are equal, (s=-12).
Step 2
Why this answer is correct
The correct answer is A. (-12). The first line has (y)-intercept (s), and the second has (-12). If they are equal, (s=-12).
Step 3
Exam Tip
पहली रेखा का (y)-अवरोध (s) और दूसरी का (-12) है। समान होने पर (s=-12) होगा।
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यदि (y=(a-4)x+a) में ढाल और (y)-अवरोध का अंतर (-4) है, तो कौन सा कथन सही है?
If in (y=(a-4)x+a), the difference between slope and (y)-intercept is (-4), which statement is correct?
#parameter_condition
#slope_intercept
#identity
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A केवल (a=4) के लिए सही है / It is true only for (a=4)
B यह हर (a) के लिए सही है / It is true for every (a)
C कोई (a) संभव नहीं / No (a) is possible
D केवल (a=0) के लिए सही है / It is true only for (a=0)
Explanation opens after your attempt
Correct Answer
B. यह हर (a) के लिए सही है / It is true for every (a)
Step 1
Concept
The slope is (a-4) and the (y)-intercept is (a). Their difference ((a-4)-a=-4) holds for every (a).
Step 2
Why this answer is correct
The correct answer is B. यह हर (a) के लिए सही है / It is true for every (a). The slope is (a-4) and the (y)-intercept is (a). Their difference ((a-4)-a=-4) holds for every (a).
Step 3
Exam Tip
ढाल (a-4) और (y)-अवरोध (a) है। उनका अंतर ((a-4)-a=-4) हर (a) के लिए है।
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रेखा (y=4x+b) बिंदुओं ( (1,9) ) और ( (3,17) ) से गुजरती है। (b) क्या है?
The line (y=4x+b) passes through ( (1,9) ) and ( (3,17) ). What is (b)?
#two_points
#intercept_given_slope
#verify
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A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
Step 1
Concept
From the first point, (9=4(1)+b). So (b=5), and the second point also fits.
Step 2
Why this answer is correct
The correct answer is B. (5). From the first point, (9=4(1)+b). So (b=5), and the second point also fits.
Step 3
Exam Tip
पहले बिंदु से (9=4(1)+b) मिलता है। इसलिए (b=5), और दूसरा बिंदु भी सही बैठता है।
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रेखा (y=mx+1) बिंदुओं ( (2,9) ) और ( (5,21) ) से गुजरती है। (m) क्या है?
The line (y=mx+1) passes through ( (2,9) ) and ( (5,21) ). What is (m)?
#two_points
#slope
#linear_form
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The slope from the two points is \(\frac{21-9}{5-2}=4\). Therefore (m=4).
Step 2
Why this answer is correct
The correct answer is C. (4). The slope from the two points is \(\frac{21-9}{5-2}=4\). Therefore (m=4).
Step 3
Exam Tip
दोनों बिंदुओं से ढाल \(\frac{21-9}{5-2}=4\) है। इसलिए (m=4) है।
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यदि (y=(k-6)x+13) और (y=5x+(k+2)) की ढालें समान हैं, तो (k) क्या है?
If (y=(k-6)x+13) and (y=5x+(k+2)) have equal slopes, what is (k)?
#compare_slopes
#parameter
#hard
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
For equal slopes, (k-6=5). This gives (k=11).
Step 2
Why this answer is correct
The correct answer is C. (11). For equal slopes, (k-6=5). This gives (k=11).
Step 3
Exam Tip
समान ढाल के लिए (k-6=5) होगा। इससे (k=11) मिलता है।
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यदि (y=(m-2 )x-5) और (y=6x+(m-9 )) का (y)-अवरोध समान है, तो (m) क्या है?
If (y=(m-2 )x-5) and (y=6x+(m-9 )) have the same (y)-intercept, what is (m)?
#compare_intercepts
#parameter
#hard
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
For equal (y)-intercepts, (-5=m-9 ). This gives (m=4).
Step 2
Why this answer is correct
The correct answer is C. (4). For equal (y)-intercepts, (-5=m-9 ). This gives (m=4).
Step 3
Exam Tip
समान (y)-अवरोध के लिए (-5=m-9 ) होगा। इससे (m=4) मिलता है।
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रेखा (y=-5x+18) में (x) कितने बढ़ाने पर (y) (35) घटेगा?
In the line (y=-5x+18), by how much must (x) increase for (y) to decrease by (35)?
#negative_slope
#change_in_x
#total_change
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The slope is (-5), so the decrease is \(5\Delta x\). From \(5\Delta x=35\), \(\Delta x=7\).
Step 2
Why this answer is correct
The correct answer is C. (7). The slope is (-5), so the decrease is \(5\Delta x\). From \(5\Delta x=35\), \(\Delta x=7\).
Step 3
Exam Tip
ढाल (-5) है, इसलिए कमी \(5\Delta x\) होगी। \(5\Delta x=35\) से \(\Delta x=7\) है।
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रेखा \(y=\frac{4}{3}x-6\) में (y) को (24) बढ़ाने के लिए (x) कितना बढ़ना चाहिए?
In the line \(y=\frac{4}{3}x-6\), how much should (x) increase to increase (y) by (24)?
#fraction_slope
#change_in_x
#rate
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A (12)
B (18)
C (24)
D (32)
Explanation opens after your attempt
Step 1
Concept
The change is \(\frac{4}{3}\Delta x=24\). This gives \(\Delta x=18\).
Step 2
Why this answer is correct
The correct answer is B. (18). The change is \(\frac{4}{3}\Delta x=24\). This gives \(\Delta x=18\).
Step 3
Exam Tip
परिवर्तन \(\frac{4}{3}\Delta x=24\) होगा। इससे \(\Delta x=18\) मिलता है।
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यदि (y=px+q) में (p=6) और (q=-8), तो सही कथन कौन सा है?
If (p=6) and (q=-8) in (y=px+q), which statement is correct?
#sign_analysis
#graph_behavior
#slope_intercept
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A रेखा घटती है और (y)-अवरोध धनात्मक है / The line decreases and the (y)-intercept is positive
B रेखा बढ़ती है और (y)-अवरोध ऋणात्मक है / The line increases and the (y)-intercept is negative
C रेखा क्षैतिज है और मूल से गुजरती है / The line is horizontal and passes through origin
D रेखा घटती है और मूल से गुजरती है / The line decreases and passes through origin
Explanation opens after your attempt
Correct Answer
B. रेखा बढ़ती है और (y)-अवरोध ऋणात्मक है / The line increases and the (y)-intercept is negative
Step 1
Concept
(p=6) gives a positive slope and (q=-8) gives a negative (y)-intercept. So the line increases.
Step 2
Why this answer is correct
The correct answer is B. रेखा बढ़ती है और (y)-अवरोध ऋणात्मक है / The line increases and the (y)-intercept is negative. (p=6) gives a positive slope and (q=-8) gives a negative (y)-intercept. So the line increases.
Step 3
Exam Tip
(p=6) धनात्मक ढाल देता है और (q=-8) ऋणात्मक (y)-अवरोध देता है। इसलिए रेखा बढ़ती है।
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यदि (5x+ay=40) का (y)-अवरोध (8) है, तो (a) क्या है?
If (5x+ay=40) has (y)-intercept (8), what is (a)?
#parameter_intercept
#standard_form
#substitution
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A (3)
B (4)
C (5)
D (8)
Explanation opens after your attempt
Step 1
Concept
Putting (x=0) gives (ay=40) and \(y=\frac{40}{a}\). From \(\frac{40}{a}=8\), (a=5).
Step 2
Why this answer is correct
The correct answer is C. (5). Putting (x=0) gives (ay=40) and \(y=\frac{40}{a}\). From \(\frac{40}{a}=8\), (a=5).
Step 3
Exam Tip
(x=0) रखने पर (ay=40) और \(y=\frac{40}{a}\) मिलता है। \(\frac{40}{a}=8\) से (a=5) है।
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यदि (bx+8y=48) की ढाल (-3) है, तो (b) क्या है?
If (bx+8y=48) has slope (-3), what is (b)?
#parameter_slope
#standard_form
#hard
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A (16)
B (20)
C (24)
D (32)
Explanation opens after your attempt
Step 1
Concept
From (8y=-bx+48), the slope is \(-\frac{b}{8}\). From \(-\frac{b}{8}=-3\), (b=24).
Step 2
Why this answer is correct
The correct answer is C. (24). From (8y=-bx+48), the slope is \(-\frac{b}{8}\). From \(-\frac{b}{8}=-3\), (b=24).
Step 3
Exam Tip
(8y=-bx+48) से ढाल \(-\frac{b}{8}\) है। \(-\frac{b}{8}=-3\) से (b=24) है।
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रेखा (y=(n-4)x+(2n-3)) का (y)-अवरोध (11) है। इसकी ढाल क्या है?
The line (y=(n-4)x+(2n-3)) has (y)-intercept (11). What is its slope?
#parameter_intercept
#find_slope
#hard
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (2n-3=11), (n=7). The slope is (n-4=3).
Step 2
Why this answer is correct
The correct answer is B. (3). From (2n-3=11), (n=7). The slope is (n-4=3).
Step 3
Exam Tip
(2n-3=11) से (n=7) मिलता है। ढाल (n-4=3) है।
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रेखा (y=(t-8)x+(t+5)) की ढाल (6) है। इसका (y)-अवरोध क्या है?
The line (y=(t-8)x+(t+5)) has slope (6). What is its (y)-intercept?
#parameter_slope
#find_intercept
#hard
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A (11)
B (12)
C (13)
D (19)
Explanation opens after your attempt
Step 1
Concept
From (t-8=6), (t=14). The (y)-intercept is (t+5=19).
Step 2
Why this answer is correct
The correct answer is D. (19). From (t-8=6), (t=14). The (y)-intercept is (t+5=19).
Step 3
Exam Tip
(t-8=6) से (t=14) मिलता है। (y)-अवरोध (t+5=19) है।
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कौन सी रेखा ( (0,-10) ) पर (y)-अक्ष काटती है और (x) के (4) बढ़ने पर (y) (28) बढ़ाती है?
Which line cuts the (y)-axis at ( (0,-10) ) and increases (y) by (28) when (x) increases by (4)?
#equation_from_rate
#intercept
#hard
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A (y=7x-10)
B (y=28x-10)
C (y=-7x-10)
D (y=7x+10)
Explanation opens after your attempt
Correct Answer
A. (y=7x-10)
Step 1
Concept
The slope is \(\frac{28}{4}=7\) and the (y)-intercept is (-10). So the line is (y=7x-10).
Step 2
Why this answer is correct
The correct answer is A. (y=7x-10). The slope is \(\frac{28}{4}=7\) and the (y)-intercept is (-10). So the line is (y=7x-10).
Step 3
Exam Tip
ढाल \(\frac{28}{4}=7\) है और (y)-अवरोध (-10) है। इसलिए रेखा (y=7x-10) है।
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कौन सी रेखा ( (0,14) ) पर (y)-अक्ष काटती है और (x) के (5) बढ़ने पर (y) (30) घटाती है?
Which line cuts the (y)-axis at ( (0,14) ) and decreases (y) by (30) when (x) increases by (5)?
#equation_from_rate
#negative_slope
#intercept
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A (y=6x+14)
B (y=-6x+14)
C (y=-30x+14)
D (y=-6x-14)
Explanation opens after your attempt
Correct Answer
B. (y=-6x+14)
Step 1
Concept
The slope is \(-\frac{30}{5}=-6\) and the (y)-intercept is (14). So (y=-6x+14) is correct.
Step 2
Why this answer is correct
The correct answer is B. (y=-6x+14). The slope is \(-\frac{30}{5}=-6\) and the (y)-intercept is (14). So (y=-6x+14) is correct.
Step 3
Exam Tip
ढाल \(-\frac{30}{5}=-6\) है और (y)-अवरोध (14) है। इसलिए (y=-6x+14) सही है।
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यदि (y=(a+4)x+(a-10)) मूल बिंदु से गुजरती है, तो इसकी ढाल क्या होगी?
If (y=(a+4)x+(a-10)) passes through the origin, what will be its slope?
#origin
#parameter
#find_slope
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A (10)
B (12)
C (14)
D (16)
Explanation opens after your attempt
Step 1
Concept
To pass through the origin, (a-10=0). Thus (a=10) and the slope is (a+4=14).
Step 2
Why this answer is correct
The correct answer is C. (14). To pass through the origin, (a-10=0). Thus (a=10) and the slope is (a+4=14).
Step 3
Exam Tip
मूल बिंदु से गुजरने के लिए (a-10=0) होगा। इसलिए (a=10) और ढाल (a+4=14) है।
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यदि (y=(2u+1)x+(u-2)) का (y)-अवरोध (6) है, तो ढाल क्या है?
If (y=(2u+1)x+(u-2)) has (y)-intercept (6), what is the slope?
#parameter_intercept
#find_slope
#linear_form
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A (15)
B (16)
C (17)
D (18)
Explanation opens after your attempt
Step 1
Concept
From (u-2=6), (u=8). The slope is (2u+1=17).
Step 2
Why this answer is correct
The correct answer is C. (17). From (u-2=6), (u=8). The slope is (2u+1=17).
Step 3
Exam Tip
(u-2=6) से (u=8) मिलता है। ढाल (2u+1=17) है।
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समीकरण (6x+7y-42=0) में (y)-अवरोध और ढाल कौन से हैं?
What are the (y)-intercept and slope in (6x+7y-42=0)?
#general_form
#fraction_slope
#y_intercept
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A (y)-अवरोध (6), ढाल \(-\frac{6}{7}\) / (y)-intercept (6), slope \(-\frac{6}{7}\)
B (y)-अवरोध (-6), ढाल \(\frac{6}{7}\) / (y)-intercept (-6), slope \(\frac{6}{7}\)
C (y)-अवरोध (42), ढाल (-6) / (y)-intercept (42), slope (-6)
D (y)-अवरोध (7), ढाल (6) / (y)-intercept (7), slope (6)
Explanation opens after your attempt
Correct Answer
A. (y)-अवरोध (6), ढाल \(-\frac{6}{7}\) / (y)-intercept (6), slope \(-\frac{6}{7}\)
Step 1
Concept
From (7y=-6x+42), \(y=-\frac{6}{7}x+6\). So the (y)-intercept is (6) and slope is \(-\frac{6}{7}\).
Step 2
Why this answer is correct
The correct answer is A. (y)-अवरोध (6), ढाल \(-\frac{6}{7}\) / (y)-intercept (6), slope \(-\frac{6}{7}\). From (7y=-6x+42), \(y=-\frac{6}{7}x+6\). So the (y)-intercept is (6) and slope is \(-\frac{6}{7}\).
Step 3
Exam Tip
(7y=-6x+42) से \(y=-\frac{6}{7}x+6\) मिलता है। इसलिए (y)-अवरोध (6) और ढाल \(-\frac{6}{7}\) है।
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यदि (y=6x+b) और (y=-4x+8) (y)-अक्ष पर एक ही बिंदु काटती हैं, तो (b) क्या है?
If (y=6x+b) and (y=-4x+8) cut the (y)-axis at the same point, what is (b)?
#same_y_intercept
#parameter
#comparison
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A (4)
B (6)
C (8)
D (10)
Explanation opens after your attempt
Step 1
Concept
The same (y)-axis point means equal (y)-intercepts. Therefore (b=8).
Step 2
Why this answer is correct
The correct answer is C. (8). The same (y)-axis point means equal (y)-intercepts. Therefore (b=8).
Step 3
Exam Tip
एक ही (y)-अक्ष बिंदु का अर्थ समान (y)-अवरोध है। इसलिए (b=8) है।
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यदि (y=ax-9) और (y=7x+3) की ढालें समान हैं, तो (x=2) पर पहली रेखा का (y) क्या होगा?
If (y=ax-9) and (y=7x+3) have equal slopes, what is (y) on the first line at (x=2)?
#compare_slopes
#evaluate_line
#parameter
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
Equal slopes give (a=7). Putting (x=2), (y=7(2)-9=5).
Step 2
Why this answer is correct
The correct answer is C. (5). Equal slopes give (a=7). Putting (x=2), (y=7(2)-9=5).
Step 3
Exam Tip
समान ढाल से (a=7) है। (x=2) रखने पर (y=7(2)-9=5) है।
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रेखा (y=-9x+c) का (y)-अवरोध (4) है। (x=-3) पर (y) क्या होगा?
The line (y=-9x+c) has (y)-intercept (4). What will (y) be at (x=-3)?
#evaluate_line
#negative_x
#intercept_given
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A (25)
B (27)
C (29)
D (31)
Explanation opens after your attempt
Step 1
Concept
The (y)-intercept (4) gives (c=4). Putting (x=-3), (y=-9(-3)+4=31).
Step 2
Why this answer is correct
The correct answer is D. (31). The (y)-intercept (4) gives (c=4). Putting (x=-3), (y=-9(-3)+4=31).
Step 3
Exam Tip
(y)-अवरोध (4) से (c=4) है। (x=-3) रखने पर (y=-9(-3)+4=31) है।
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यदि रेखा (y=(k-3)x+2) (x) के (6) बढ़ने पर (y) (48) बढ़ाती है, तो (k) क्या है?
If the line (y=(k-3)x+2) increases (y) by (48) when (x) increases by (6), what is (k)?
#parameter_slope
#total_change
#hard
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A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
The slope is (k-3) and (6(k-3)=48). Therefore (k-3=8) and (k=11).
Step 2
Why this answer is correct
The correct answer is C. (11). The slope is (k-3) and (6(k-3)=48). Therefore (k-3=8) and (k=11).
Step 3
Exam Tip
ढाल (k-3) है और (6(k-3)=48)। इसलिए (k-3=8) और (k=11) है।
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यदि रेखा (y=-(p-1)x+16) (x) के (5) बढ़ने पर (y) (35) घटाती है, तो (p) क्या है?
If the line (y=-(p-1)x+16) decreases (y) by (35) when (x) increases by (5), what is (p)?
#parameter_slope
#negative_slope
#total_change
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The slope is (-(p-1)), and the decrease is (5(p-1)=35). So (p-1=7) and (p=8).
Step 2
Why this answer is correct
The correct answer is C. (8). The slope is (-(p-1)), and the decrease is (5(p-1)=35). So (p-1=7) and (p=8).
Step 3
Exam Tip
ढाल (-(p-1)) है और कमी (5(p-1)=35) होगी। इसलिए (p-1=7) और (p=8) है।
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समीकरण (7y-4x=21) में (x=0) पर (y) का मान और ढाल क्या हैं?
In (7y-4x=21), what are the value of (y) at (x=0) and the slope?
#rearrange_equation
#value_at_zero
#slope
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A (y=3), ढाल \(\frac{4}{7}\) / (y=3), slope \(\frac{4}{7}\)
B (y=-3), ढाल \(-\frac{4}{7}\) / (y=-3), slope \(-\frac{4}{7}\)
C (y=21), ढाल (4) / (y=21), slope (4)
D (y=7), ढाल (-4) / (y=7), slope (-4)
Explanation opens after your attempt
Correct Answer
A. (y=3), ढाल \(\frac{4}{7}\) / (y=3), slope \(\frac{4}{7}\)
Step 1
Concept
From (7y=4x+21), \(y=\frac{4}{7}x+3\). So at (x=0), (y=3) and the slope is \(\frac{4}{7}\).
Step 2
Why this answer is correct
The correct answer is A. (y=3), ढाल \(\frac{4}{7}\) / (y=3), slope \(\frac{4}{7}\). From (7y=4x+21), \(y=\frac{4}{7}x+3\). So at (x=0), (y=3) and the slope is \(\frac{4}{7}\).
Step 3
Exam Tip
(7y=4x+21) से \(y=\frac{4}{7}x+3\) मिलता है। इसलिए (x=0) पर (y=3) और ढाल \(\frac{4}{7}\) है।
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यदि (y=mx+c) में (m+c=15) और (c=6), तो ढाल क्या है?
If (m+c=15) and (c=6) in (y=mx+c), what is the slope?
#slope_intercept_relation
#parameter
#hard
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Putting (c=6) gives (m+6=15). Therefore (m=9), which is the slope.
Step 2
Why this answer is correct
The correct answer is D. (9). Putting (c=6) gives (m+6=15). Therefore (m=9), which is the slope.
Step 3
Exam Tip
(c=6) रखने पर (m+6=15) मिलता है। इसलिए (m=9), जो ढाल है।
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यदि (y=mx+c) में ढाल (-5) है और (m+c=2), तो (y)-अवरोध क्या है?
If the slope is (-5) and (m+c=2) in (y=mx+c), what is the (y)-intercept?
#slope_intercept_relation
#find_intercept
#hard
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A (5)
B (6)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
Slope (-5) gives (m=-5). From (-5+c=2), (c=7), which is the (y)-intercept.
Step 2
Why this answer is correct
The correct answer is C. (7). Slope (-5) gives (m=-5). From (-5+c=2), (c=7), which is the (y)-intercept.
Step 3
Exam Tip
ढाल (-5) से (m=-5) है। (-5+c=2) से (c=7), जो (y)-अवरोध है।
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रेखा \(y=\frac{3}{4}x+c\) बिंदु ( (8,10) ) से गुजरती है। (c) क्या है?
The line \(y=\frac{3}{4}x+c\) passes through ( (8,10) ). What is (c)?
#fraction_slope
#find_intercept
#point_given
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
Substituting the point gives (10=\frac{3}{4}(8)+c). So (10=6+c) and (c=4).
Step 2
Why this answer is correct
The correct answer is C. (4). Substituting the point gives (10=\frac{3}{4}(8)+c). So (10=6+c) and (c=4).
Step 3
Exam Tip
बिंदु रखने पर (10=\frac{3}{4}(8)+c) मिलता है। इसलिए (10=6+c) और (c=4) है।
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रेखा (y=mx-4) बिंदु ( (10,1) ) से गुजरती है। (m) क्या है?
The line (y=mx-4) passes through ( (10,1) ). What is (m)?
#find_slope
#point_given
#fraction_slope
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A \(\frac{1}{2}\)
B \(\frac{3}{5}\)
C \(\frac{5}{2}\)
D \(\frac{1}{5}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
Substituting the point gives (1=10m-4). Thus (10m=5) and \(m=\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). Substituting the point gives (1=10m-4). Thus (10m=5) and \(m=\frac{1}{2}\).
Step 3
Exam Tip
बिंदु रखने पर (1=10m-4) मिलता है। इससे (10m=5) और \(m=\frac{1}{2}\) है।
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यदि (y=(4a-1)x+(a+2)) का (y)-अवरोध (9) है, तो ढाल क्या है?
If (y=(4a-1)x+(a+2)) has (y)-intercept (9), what is the slope?
#parameter_intercept
#find_slope
#linear_form
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A (25)
B (26)
C (27)
D (28)
Explanation opens after your attempt
Step 1
Concept
From (a+2=9), (a=7). The slope is (4a-1=27).
Step 2
Why this answer is correct
The correct answer is C. (27). From (a+2=9), (a=7). The slope is (4a-1=27).
Step 3
Exam Tip
(a+2=9) से (a=7) मिलता है। ढाल (4a-1=27) है।
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यदि (y=(b-9)x+(3b-2)) की ढाल (1) है, तो (y)-अवरोध क्या है?
If (y=(b-9)x+(3b-2)) has slope (1), what is the (y)-intercept?
#parameter_slope
#find_intercept
#linear_form
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A (26)
B (28)
C (30)
D (32)
Explanation opens after your attempt
Step 1
Concept
From (b-9=1), (b=10). The (y)-intercept is (3b-2=28).
Step 2
Why this answer is correct
The correct answer is B. (28). From (b-9=1), (b=10). The (y)-intercept is (3b-2=28).
Step 3
Exam Tip
(b-9=1) से (b=10) मिलता है। (y)-अवरोध (3b-2=28) है।
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समीकरण (3x-4y+12=0) की ढाल और (y)-अवरोध क्या हैं?
What are the slope and (y)-intercept of (3x-4y+12=0)?
#general_form
#fraction_slope
#rearrange
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A ढाल \(\frac{3}{4}\), (y)-अवरोध (3) / Slope \(\frac{3}{4}\), (y)-intercept (3)
B ढाल \(-\frac{3}{4}\), (y)-अवरोध (-3) / Slope \(-\frac{3}{4}\), (y)-intercept (-3)
C ढाल (4), (y)-अवरोध \(\frac{3}{4}\) / Slope (4), (y)-intercept \(\frac{3}{4}\)
D ढाल (3), (y)-अवरोध (-12) / Slope (3), (y)-intercept (-12)
Explanation opens after your attempt
Correct Answer
A. ढाल \(\frac{3}{4}\), (y)-अवरोध (3) / Slope \(\frac{3}{4}\), (y)-intercept (3)
Step 1
Concept
From (-4y=-3x-12), \(y=\frac{3}{4}x+3\). So the slope is \(\frac{3}{4}\) and the (y)-intercept is (3).
Step 2
Why this answer is correct
The correct answer is A. ढाल \(\frac{3}{4}\), (y)-अवरोध (3) / Slope \(\frac{3}{4}\), (y)-intercept (3). From (-4y=-3x-12), \(y=\frac{3}{4}x+3\). So the slope is \(\frac{3}{4}\) and the (y)-intercept is (3).
Step 3
Exam Tip
(-4y=-3x-12) से \(y=\frac{3}{4}x+3\) मिलता है। इसलिए ढाल \(\frac{3}{4}\) और (y)-अवरोध (3) है।
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यदि (y=(t+2)x-6) और (y=9x+(2t-1)) की ढालें समान हैं, तो दूसरी रेखा का (y)-अवरोध क्या है?
If (y=(t+2)x-6) and (y=9x+(2t-1)) have equal slopes, what is the (y)-intercept of the second line?
#compare_slopes
#find_intercept
#parameter
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A (11)
B (13)
C (15)
D (17)
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Step 1
Concept
Equal slopes give (t+2=9) and (t=7). The second line's (y)-intercept is (2t-1=13).
Step 2
Why this answer is correct
The correct answer is B. (13). Equal slopes give (t+2=9) and (t=7). The second line's (y)-intercept is (2t-1=13).
Step 3
Exam Tip
समान ढाल से (t+2=9) और (t=7) है। दूसरी रेखा का (y)-अवरोध (2t-1=13) है।
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यदि (y=3x+(v-5)) और (y=(v+2)x+6) का (y)-अवरोध समान है, तो दूसरी रेखा की ढाल क्या है?
If (y=3x+(v-5)) and (y=(v+2)x+6) have the same (y)-intercept, what is the slope of the second line?
#compare_intercepts
#find_slope
#parameter
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A (11)
B (12)
C (13)
D (14)
Explanation opens after your attempt
Step 1
Concept
Equal (y)-intercepts give (v-5=6) and (v=11). The slope of the second line is (v+2=13).
Step 2
Why this answer is correct
The correct answer is C. (13). Equal (y)-intercepts give (v-5=6) and (v=11). The slope of the second line is (v+2=13).
Step 3
Exam Tip
समान (y)-अवरोध से (v-5=6) और (v=11) है। दूसरी रेखा की ढाल (v+2=13) है।
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रेखा \(y=-\frac{4}{3}x+12\) में (y) को (28) घटाने के लिए (x) कितना बढ़ना चाहिए?
In the line \(y=-\frac{4}{3}x+12\), how much should (x) increase to decrease (y) by (28)?
#negative_fraction_slope
#change_in_x
#rate
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A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
The decrease is \(\frac{4}{3}\Delta x\). From \(\frac{4}{3}\Delta x=28\), \(\Delta x=21\).
Step 2
Why this answer is correct
The correct answer is D. (21). The decrease is \(\frac{4}{3}\Delta x\). From \(\frac{4}{3}\Delta x=28\), \(\Delta x=21\).
Step 3
Exam Tip
कमी \(\frac{4}{3}\Delta x\) होगी। \(\frac{4}{3}\Delta x=28\) से \(\Delta x=21\) मिलता है।
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यदि (y=(k+5)x+3) (x) के (3) बढ़ने पर (y) (27) बढ़ाती है, तो (k) क्या है?
If (y=(k+5)x+3) increases (y) by (27) when (x) increases by (3), what is (k)?
#parameter_slope
#total_change
#solve
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A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
Step 1
Concept
The slope is (k+5) and (3(k+5)=27). Therefore (k+5=9) and (k=4).
Step 2
Why this answer is correct
The correct answer is B. (4). The slope is (k+5) and (3(k+5)=27). Therefore (k+5=9) and (k=4).
Step 3
Exam Tip
ढाल (k+5) है और (3(k+5)=27)। इसलिए (k+5=9) और (k=4) है।
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यदि (y=mx+c) में (c=-9) और (m-c=16), तो ढाल क्या है?
If (c=-9) and (m-c=16) in (y=mx+c), what is the slope?
#slope_intercept_relation
#parameter
#hard
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
Putting (c=-9) gives (m-(-9)=16). So (m+9=16) and (m=7).
Step 2
Why this answer is correct
The correct answer is C. (7). Putting (c=-9) gives (m-(-9)=16). So (m+9=16) and (m=7).
Step 3
Exam Tip
(c=-9) रखने पर (m-(-9)=16) मिलता है। इसलिए (m+9=16) और (m=7) है।
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यदि (y=mx+c) में (m=-3) और (3c+m=18), तो (y)-अवरोध क्या है?
If (m=-3) and (3c+m=18) in (y=mx+c), what is the (y)-intercept?
#slope_intercept_relation
#find_intercept
#hard
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A (5)
B (6)
C (7)
D (8)
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Step 1
Concept
Putting (m=-3) gives (3c-3=18). Thus (3c=21) and (c=7).
Step 2
Why this answer is correct
The correct answer is C. (7). Putting (m=-3) gives (3c-3=18). Thus (3c=21) and (c=7).
Step 3
Exam Tip
(m=-3) रखने पर (3c-3=18) मिलता है। इससे (3c=21) और (c=7) है।
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