Question

graph the line that passes through the points (-7, 7) and (-7, -4) and determine the equation of the line.

Explanation:

Step1: Analyze the x - coordinates of the points

The two points are \((-7,7)\) and \((-7, - 4)\). We can see that the x - coordinate for both points is \(-7\). In a line, if the x - coordinate of all points on the line is the same, the line is a vertical line.

Step2: Determine the equation of the vertical line

The general equation of a vertical line is \(x = a\), where \(a\) is the x - coordinate of any point on the line. Since the x - coordinate of the given points is \(-7\), the equation of the line is \(x=-7\).

Step3: Graph the line (description)

To graph the line \(x = - 7\), we draw a vertical line that passes through all points with an x - coordinate of \(-7\). On the given coordinate plane, we find the point \((-7,7)\) and \((-7,-4)\) and draw a straight vertical line connecting (and extending beyond) these points.

Answer:

The equation of the line is \(x = - 7\). To graph it, draw a vertical line through \(x=-7\) (passing through \((-7,7)\) and \((-7,-4)\) and extending in both vertical directions).