Question

Line $m$ has a negative slope and a negative $y$-intercept. Line $n$ is parallel to line $m$ and has a positive $y$-intercept. The $x$-intercept of $n$ must be

• A. negative and greater than the $x$-intercept of $m$
• B. negative and less than the $x$-intercept of $m$
• C. zero
• D. positive and greater than the $x$-intercept of $m$
• E. positive and less than the $x$-intercept of $m$

Answer 1

The correct option is D positive and greater than the $x$-intercept of $m$

The slope of $m$ is negative and the line has negative $y$-intercept, which implies the line $m$ has negative $x$-intercept and the line lies in $2^{nd}$, $3^{rd}$, $4^{th}$ quadrants
Given that line $n$ is parallel to $m$ and has positive $y$-intercept , which implies the line shifts upwards by some distance, which means it lies in $1^{st}$, $2^{nd}$, $4^{th}$ quadrants.
So the line $n$ has positive $x$-intercept and greater than $x$ -intercept of $m$
So, the correct option is $D$.