Question

If a line with y-intercept $2$, is perpendicular to the line $3x-2y=6$, then its x-intercept is

• A. $1$
• B. $2$
• C. $-4$
• D. $3$

Answer 1

The correct option is D

$3$

Explanation for the correct option:

Step 1. Find the x-intercept of the line:

Given, $3x–2y=6$

$\Rightarrow$ $y=\left(\frac{3}{2}\right)x–3$

Here, slope $m_1=\frac{3}{2}$

$\therefore$Slope of perpendicular line, $m_2=\frac{-2}{3}$ $\left[\mathbf{\because }{\mathit{m}}_{\mathbf{1}}{\mathit{m}}_{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{1}\right]$

Also given that y intercept $=2$

That means it pass through $A(0,2)$

Step 2. Let $h$ be the x intercept.

$\Rightarrow B=(h,0)$

Now,

Slope of AB, $m_2=\frac{(0–2)}{h}$

$\Rightarrow$ $\frac{-2}{3}=\frac{-2}{h}$

$\mathbf{\therefore }\mathit{h}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}$

Hence, Option ‘D’ is Correct.