Question

If the line passing through $(4,3)$ and $(2,k)$ is perpendicular to $y=2x+3$, then $k=?$

• A. $-1$
• B. $1$
• C. $-4$
• D. $4$

Answer 1

The correct option is D

$4$

Explanation for correct option

Step 1: Evaluate the slope of the given points

Given points are $(4,3)$ and $(2,k)$

Let the slope be $m_1=\frac{y_2-y_1}{x_2-x_1}$

So, $m_1=\frac{k-3}{2-4}=\frac{k-3}{-2}$

Step 2: Evaluate the slope of the given line

Given equation of the line, $y=2x+3$

Let the slope-intercept form of line be $y=m_{2}x+b$

So, $m_2=2$

Step 3: Solve for the given variable

It is given that the points joining together are perpendicular to the equation of the line

So, $m_1\times m_2=-1$

$$\begin{gathered} \Rightarrow \left(\frac{k-3}{-2}\right)\times 2=-1 \\ \Rightarrow k-3=1 \\ \Rightarrow k=4 \end{gathered}$$

Therefore, option (D) is the correct answer.