Question

graph the line that passes through the points (-1, 7) and (-1, -1) and determine the equation of the line.

Explanation:

Step1: Analyze x - coordinates

Both points \((-1, 7)\) and \((-1, -1)\) have the same x - coordinate (\(x=-1\)).

Step2: Determine line type

A line with all points having 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 the given points is \(-1\), the equation of the line is \(x=-1\). For graphing, we draw a vertical line passing through \(x = - 1\) on the coordinate plane, which will pass through both \((-1,7)\) and \((-1,-1)\).

Answer:

The equation of the line is \(x=-1\), and the graph is a vertical line passing through \(x = - 1\) (passing through the points \((-1,7)\) and \((-1,-1)\)).