Question

writing the equation of a line perpendicular to the y - axis
complete the statements using the drop - down menus.
the line perpendicular to the y - axis through the point (-4, -2) is y = - 2
the slope of this line is 0

Explanation:

Step1: Recall line - axis relationship

A line perpendicular to the y - axis is a horizontal line. The equation of a horizontal line passing through the point $(x_0,y_0)$ is of the form $y = y_0$. Given the point $(-4,-2)$, the equation of the line is $y=-2$.

Step2: Recall slope formula for horizontal line

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For a horizontal line, $y_1=y_2$. So, if we take two points on the line $y = - 2$, say $(-4,-2)$ and $(0,-2)$, then $m=\frac{-2-(-2)}{0 - (-4)}=\frac{0}{4}=0$.

Answer:

The line perpendicular to the $y$-axis through the point $(-4,-2)$ is $y = - 2$. The slope of this line is $0$.