write an equation of the line that passes through the pair of points. (-6, 5), (-6, -4)

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For the points $(-6,5)$ and $(-6,-4)$, $x_1=-6,y_1 = 5,x_2=-6,y_2=-4$. Then $m=\frac{-4 - 5}{-6-(-6)}=\frac{-9}{0}$, which is undefined.

Step2: Determine the line equation

Since the slope is undefined, the line is a vertical line. The equation of a vertical line passing through the point $(x_0,y_0)$ is $x = x_0$. Here $x_0=-6$. So the equation of the line is $x=-6$.

Answer:

$x=-6$