Question

Consider the line y=5/7x+7. Find the equation for the line that is parallel to the line and passes through the point (-5,-2). Find the equation for the line that is perpendicular to the line and passes through the point (-5,-2).

Answer 1

The parallel line:
y = mx + c
y = 5/7x + 7

Gradient of parallel line = 5/7

y = mx + c
y = 5/7x + c
-2 = (5/7 x -5) + c
-2 = -25/7 + c
-2 + 25/7 = c
c = 11/7

y = 5/7x + 11/7

The perpendicular line
y = mx + c
y = 5/7x + c
m = 5/7

Gradient of perpendicular line = -1/(5/7) = -7/5

y = mx + c
y = -7/5x + c
-2 = (-7/5 x -5) + c
-2 = 7 + c
-2 - 7 = c
c = -9

y = -7/5x - 9