Answer:
x = -2
Explanation:
Given the point, (-2, 9) and the linear equation of a horizontal line, y = 6:
The linear equation of a horizontal line with a slope of zero (m = 0) is y = b, for which the y-intercept is (0, b). Perpendicular lines comprise of the intersection of two lines forming 90° angles.
Since we are given the equation of a horizontal line, then we can assume that the line that intersects a horizontal line must be a vertical line in order to form perpendicular lines.
The linear equation of a vertical line with an undefined slope is x = a, for which the x-intercept is (a, 0). Vertical lines have an undefined slope because these lines do not have any horizontal change. Thus, when you try to solve for its slope, the denominator will have a difference of 0, making the mathematical operation undefined.
We can use the x-coordinate of the given point, (-2, 9), to formulate an equation for a vertical line: x = -2.
Therefore, the equation of the line that goes through y = 6 is x = -2.
Attached is a screenshot of the graph of both equations, y = 6 and x = -2, showing that their intersection form 90° angles, making them perpendicular lines.