Questions: What is an equation of the line that passes through the points (-2,5) and (-2,-8)?

Transcript text: What is an equation of the line that passes through the points $(-2,5)$ and $(-2,-8)$ ?

Solution

Solution Steps

To find the equation of a line that passes through two points, we first determine the slope. However, if the x-coordinates of both points are the same, the line is vertical. In this case, the equation of the line is simply $ x = \text{constant} $, where the constant is the x-coordinate of the points.

Step 1: Identify the Type of Line

Given the points $(-2, 5)$ and $(-2, -8)$, we observe that both points have the same x-coordinate, $-2$. This indicates that the line passing through these points is vertical.

Step 2: Determine the Equation of the Line

For a vertical line, the equation is of the form $x = \text{constant}$. Since the x-coordinate for both points is $-2$, the equation of the line is $x = -2$.