Question

What is the equation, in slope-intercept form, of the line that is perpendicular to the line y – 4 = –(x – 6) and passes through the point (−2, −2)? y = –x – y = –x + y = x – 1 y = x + 1

Answer 1

Let's convert the equation in point-slope form to slope-intercept form.

y - 4 = -(x - 6)
Multiply everything out.
y - 4 = -x + 6
Add 4 to both sides.
y = -x + 10

To be perpendicular, the slope of the new has to be the reciprocal of the other line. To slope in this equation is -1/1. To get the reciprocal, flip the numerator and denominator and change the sign too.

-1/1 becomes 1/-1, and changes to 1/+1, or 1.

y = x + b

Input the coordinate point and solve for b.

-2 = -2 + b
Add 2 to both sides.
0 = b

y = x