Question

what is an equation of the line that passes through the points (3,5) and (3, - 8)?

Explanation:

Step1: Calculate the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1 = 3,y_1 = 5,x_2 = 3,y_2=-8$. So $m=\frac{-8 - 5}{3 - 3}=\frac{-13}{0}$, which is undefined.

Step2: Determine the line equation

Since the slope is undefined, the line is a vertical line. For a vertical line passing through the point $(a,b)$, the equation of the line is $x=a$. The $x$-coordinate of both given points is 3. So the equation of the line is $x = 3$.

Answer:

$x = 3$