Question

Graph the two lines in the same coordinate plane. Then find the coordinates of the point at which the lines cross. \(x=-5, y=2\)

Short answer

The coordinates of the point at which the two lines intersect are (-5, 2).

Step-by-step solution

Analyze the given lines

Notice that the lines \(x=-5\) and \(y=2\) are not the typical form of linear equations (y = mx + b). Both equations only contain one variable. \(x=-5\) is a vertical line passing through the point at -5 on the x-axis. \(y=2\) is a horizontal line passing through the point at 2 on the y-axis. This distinction becomes important when sketching the graphs.

Graphing the lines on the same coordinate plane

Start to draw a Cartesian plane (a plain with x and y axes). The first line to graph is \(x=-5\). This is a vertical line passing through the point -5 on the x-axis. The second line, \(y=2\), is a horizontal line passing through the point 2 on the y-axis. Draw these on the same plane.

Identify the intersection

The two lines intersect at the point where \(x=-5\) and \(y=2\). Therefore, the point of intersection is (-5, 2)