Question

The $x$-intercept of a line is $-2$. The line has a slope of $\frac{-3}{2}$. Find the equation of this line.

• A. $y=\frac{-3}{2}x-3$
• B. $y=\frac{3}{2}x-3$
• C. $x=\frac{-3}{2}y-3$
• D. $y=\frac{-3}{2}x+3$

Answer 1

The correct option is A $y=\frac{-3}{2}x-3$

Given, the $x$-intercept of the line is $-2$. This implies that the line passes through (-2,0), since the $y$-coordinate is 0 at the $x$-intercept.
The line crosses $x$-axis at $(-2,0)$ with a slope of $\frac{-3}{2}.$
As point and slope are given, we will use point slope form of a line.
The point slope form of a line is given as:
$y-y_1=m(x-x_1)$
where 'm' is the slope and $(x_1,y_1)$ is the point from which the line is passing.

Slope $=\frac{-3}{2}$ and point $=(-2,0)$

Equation of line: $y-0=\frac{-3}{2}(x-(-2\left)\right)$
$y=\frac{-3}{2}(x+2)$

$y=\left(\frac{-3}{2}x\right)+(\frac{-3}{2}\times 2)$

$y=\frac{-3}{2}x-3$
Hence, the equation of line is $y=\frac{-3}{2}x-3$
Option (a) is correct.