Question : What is the equation of the line perpendicular to the line $2x+3y=-6$ and having y-intercept 3?
Option 1: $3x-2y=6$
Option 2: $3x-2y=-6$
Option 3: $2x-3y=-6$
Option 4: $2x-3y=6$
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Correct Answer: $3x-2y=-6$
Solution :
The equation of the given line is $2x+3y=–6$
The y-intercept is $3$.
According to the question,
A line with slope $m$ is represented as $y=mx+c$
Given line, $2x+3y=–6$
⇒ $y=-\frac{2}{3}x-2$
Slope of the line $=–\frac{2}{3}$
The product of the slope of two perpendicular lines is $–1$.
So, the slope of the required line is $=(–\frac{1}{–\frac{2}{3}}) = \frac{3}{2}$
The equation of the line is
$y=\frac{3}{2}x+c$
Given y-intercept ($c$) $=3$,
Now, $ y=\frac{3}{2}x + 3$
⇒ $2y=3x+6$
Therefore, the equation of the required line is $3x-2y=-6$
Hence, the correct answer is $3x-2y=-6$.
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