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