Write the equation of the line with the given characteristics Perpendicular to x = - 5 passes through (- 8, 13)

This is a complicated problem, so I hope you read through my explanation and find it helpful.

Given x = -5, and the point (-8, 13):

x = -5 is a vertical line.

Vertical lines are symbolically represented by the equation, x = a where a is the x-intercept.

Vertical lines have undefined slope. Since any two points on a vertical line have the same x-coordinate (x = -5), the slope of the equation cannot be computed as a finite number according to the slope formula, m = (y2 - y1)/(x2 - x1), because division by zero is an undefined operation.

Perpendicular lines have slopes that are negative reciprocals of one another (meaning, multiplying the slopes of both lines will have a product of -1).

However, because x = -5 is a vertical line, then it means that the other line perpendicular to it must be a HORIZONTAL LINE, so that they intersect at a 90° angle and qualify as perpendicular lines.

Horizontal lines are symbolically represented by the equation, y = b where b is the y-intercept. Therefore, to come up with a horizontal line, you must use the y-coordinate of point, (-8, 13), to come up with the equation, y = 13.

Therefore, the equation of the perpendicular line is y = 13.

As a proof, I’m including a screenshot of the graphed equations, which also contains the given point, (-8, 13).

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