Question

graph the line that passes through the points (-8, -2) and (-8, 1) and determine the equation of the line.

Explanation:

Step1: Analyze the x - coordinates of the points

The two points are \((-8, -2)\) and \((-8, 1)\). We can see that the x - coordinate for both points is \(x=-8\), and the y - coordinates are different (\(y = - 2\) and \(y=1\)).

Step2: Determine the type of line

A line where all the points have the same x - coordinate is a vertical line. The equation of a vertical line is of the form \(x = a\), where \(a\) is the x - coordinate of any point on the line. Since the x - coordinate of both given points is \(-8\), the equation of the line is \(x=-8\).
To graph the line, we draw a vertical line passing through \(x = - 8\) on the coordinate plane. This line will pass through all points with \(x=-8\) regardless of the value of \(y\).

Answer:

The equation of the line is \(x=-8\) (and the graph is a vertical line passing through \(x = - 8\) on the coordinate plane).