Answer:
he line y = -8 is horizontal
The line perpendicular to the line y = -8 is vertical
The equation of the line perpendicular to the line y = -8 through
the point (-4 , -2) is x = -4
Explanation:
Let us revise some notes about the vertical and horizontal lines
The equation of a horizontal line passes through point (a , b) is y = b, because the y-coordinates of all points on the line are equal
The equation of a vertical line passes through point (a , b) is x = a, because the x-coordinates of all points on the line are equal
The horizontal line and the vertical line are perpendicular to each other
We need to find the equation of the line perpendicular to the line y = -8 through the point (-4 , -2)
∵ The equation of the given line is y = -8
∴ The given line is a horizontal line
The line y = -8 is horizontal
∵ The line y = -8 is a horizontal
∴ The line perpendicular to it must be vertical
The line perpendicular to the line y = -8 is vertical
∵ The equation of a vertical line is x = a, where a is the x-coordinate
of a point lies on the line
∵ The line perpendicular to the line y = -8 through the point (-4 , -2)
∴ a = -4
∴ The equation of the perpendicular line is x = -4
The equation of the line perpendicular to the line y = -8 through
the point (-4 , -2) is x = -4