Question

Consider the line y=-4/7x+4.

Find the equation of the line that is parallel to this line and passes through the point (7,-4).
Find the equation of the line that is perpendicular to this line and passes through the point (7,-4).

Answer 1

1). y = -4/7x 2). y = 7/4x - 65/4

Explanation:

1). When a line is parallel, the slope remains the same.

y = -4/7x + b

-4 = -4/7(7) + b

-4 = -4 + b

0 = b

The equation is simply y = -4/7x.

2). When a line is perpendicular, the slope becomes the exact opposite.

y = 7/4x + b

-4 = 7/4(7) + b

-4 = 49/4 + b

-65/4 = b

The equation is y = 7/4x - 65/4.