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29 Jan 2021, 11:41
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
79% (01:51) correct
21%
(01:41)
wrong
based on 70
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What is the equation of a line whose intercepts are twice of the line 3x – 2y – 12 = 0 ?
(A) 3x – 2y = 24
(B) 3x – 4y = 12
(C) 3x – 3y = 24
(D) 2x – 3y = 18
(E) 2x – y = 12
(A) 3x – 2y = 24
(B) 3x – 4y = 12
(C) 3x – 3y = 24
(D) 2x – 3y = 18
(E) 2x – y = 12
\(3x – 2y – 12 = 0 \)
After rearranging the above equation:
\(\dfrac{3x}{12} + \dfrac{(-2y)}{12} = \dfrac{12}{12} \)
\(\dfrac{x}{4} + \dfrac{y}{(-6)} = 1\)
Intersection points at x-axis is \((4,0)\) and y-axis is \((0,-6)\).
NOTE: This is derived from the standard form of the equation of a straight line, often called the intercept form of a line. And the formula is, \( \dfrac{x}{a} + \dfrac{y}{b} = 1\), which is used to represent a line that intersects the x-axis at \((a,0)\) and the y-axis at \((0,b)\).
Required - The line whose intercepts are twice, i.e, x-axis \(2\times (4, 0)\) and y-axis \(2\times (0, -6)\). Therefore, using the above intercept form of a line we can rewrite the equations as:
\(\frac{x}{8 }+ \frac{y}{(-12)}=1\)
\(-12x + 8y = -96\)
\(3x – 2y = 24\)
ANS A
Edited with a better explanation.
After rearranging the above equation:
\(\dfrac{3x}{12} + \dfrac{(-2y)}{12} = \dfrac{12}{12} \)
\(\dfrac{x}{4} + \dfrac{y}{(-6)} = 1\)
Intersection points at x-axis is \((4,0)\) and y-axis is \((0,-6)\).
NOTE: This is derived from the standard form of the equation of a straight line, often called the intercept form of a line. And the formula is, \( \dfrac{x}{a} + \dfrac{y}{b} = 1\), which is used to represent a line that intersects the x-axis at \((a,0)\) and the y-axis at \((0,b)\).
Required - The line whose intercepts are twice, i.e, x-axis \(2\times (4, 0)\) and y-axis \(2\times (0, -6)\). Therefore, using the above intercept form of a line we can rewrite the equations as:
\(\frac{x}{8 }+ \frac{y}{(-12)}=1\)
\(-12x + 8y = -96\)
\(3x – 2y = 24\)
ANS A
Edited with a better explanation.
General Discussion
07 Feb 2021, 06:38
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The best way to solve this is to look at the slope of the equation because it is going to be the same and find the option that is going to reflect the same equation
