Question

NEED HELP ASAP Consider the line y= -4x + 4.

Find the equation of the line that is parallel to this line and passes through the point (−6, -4)
Find the equation of the line that is perpendicular to this line and passes through the point (−6, 4.)

Answer 1

• parallel: y +4 = -4(x +6)
• perpendicular: y -4 = 1/4(x +6)

Explanation:

You want the equations of the lines parallel and perpendicular to y=-4x+4 through the points (-6, -4) and (-6, 4), respectively.

Slope relations

The equation of the given line is in slope-intercept form. This means its slope is the coefficient of x: -4.

Parallel lines have the same slope, so the parallel line will have slope -4.

Perpendicular lines have opposite reciprocal slopes, so the perpendicular line will have slope -1/(-4) = 1/4.

Point-slope equation

The point-slope equation of a line is ...

y -k = m(x -h) . . . . . . line with slope m through point (h, k)

This problem gives you a point on each line, and we know the required slope, so this form of the equation for a line is just what we need.

Parallel line

m = -4, (h, k) = (-6, -4)

y +4 = -4(x +6)

Perpendicular line

m = 1/4, (h, k) = (-6, 4)

y -4 = 1/4(x +6)