91Ó°ÊÓ

The equation of line in slope-intercept form is:

$y=mx+b$

Where$m$ is the slope of the line and$b$ is the $y$-intercept of the line.

The $x$-intercept of the line having equation$y=mx+b$ is given by:

role="math" localid="1647350556794" $$\begin{gathered} 0=mx+b \\ −b=mx \\ \frac{−b}{m}=x \\ −\frac{y−\text{intercept}}{slope}=x \end{gathered}$$

Therefore, the $x$-intercept of the line having equation$y=mx+b$ is given by $−\frac{y−\text{intercept}}{slope}$.

Let the initial slope and $y$-intercept of the line be $m$and $b$.

Therefore, the initial $x$-intercept of the line is:

role="math" localid="1647350686579" $$\begin{gathered} \text{initial}x−\text{intercept}=−\frac{y−\text{intercept}}{slope} \\ =−\frac{b}{m} \end{gathered}$$

It is given that the slope and $y$-intercept of the line have been doubled.

Therefore, the final slope and $y$-intercept of the line are$2m$ and $2b$.

Therefore, the final $x$-intercept of the line is:

role="math" localid="1647350786311" $$\begin{gathered} \text{final}x−\text{intercept}=−\frac{y−\text{intercept}}{slope} \\ =−\frac{2b}{2m} \\ =−\frac{b}{m} \end{gathered}$$

Therefore, it can be noticed that the initial $x$-intercept of the line is equal to the final $x$-intercept of the line.

Therefore, the $x$-intercept remains the same.

Therefore, the option J is correct.