Question

Given the graph of a line y=−x. Write an equation of a line which is perpendicular and goes through the point (8,2).

Answer 1

When a line is perpendicular to another line, the slope is the negative reciprocal of the other line's slope. So in this case, the slope would be 1, since the negative reciprocal of -1 is 1/1 which is 1.

To find the y-intercept, you have to substitute the point (8,2) into y = mx + b

2 = 1(8) + b

b = -6

The equation is y = x - 6

Answer 2

Y=-x
Gradient=-1

(8,2) x=8 and y=2

Perpendicular lines of them:

x=1/-8 and y=-0.5

Put them into a basic line equation

-0.5=(-1x-0.125)+c —> -0.5= 0.125+c —>
-0.375=c

The equation is y=-x - 0.375