Answer:
x = -2
Step-by-step explanation:
Given the point, (-2, 9) and the linear equation of a <u>horizontal line</u>, y = 6:
The linear equation of a horizontal line with a slope of zero (<em>m</em> = 0) is y = <em>b, </em>for which the y-intercept is (0, <em>b</em>). <u>Perpendicular lines</u> 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 <em>the line that intersects a horizontal line must be a </em><u><em>vertical line</em></u> in order to form perpendicular lines.
The linear equation of a <u>vertical line</u> with an undefined slope is <em>x</em> = <em>a</em>, for which the x-intercept is (<em>a</em>, 0). Vertical lines have an <u>undefined slope </u>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 <u>x-coordinate</u> 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.
