Determine the equation of the line perpendicular to the line y = –8 through the point (–4, –2).

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

Step-by-step 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

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step-by-step explanation: