Question

Find the equation of the line through the point ( 3 , − 7 ) that is perpendicular to the line with equation y = x − 12 .

Answer 1

Answer:  y = -x - 4

Step-by-step explanation:

A perpendicular line has a slope that is the negative inverse of the reference line, which is y = x-12.  The slope here is 1, so the negative inverse would be -1/1, or -1.  The perpendicular line would therefore be:

y = -1x + b

We can find b by using the given point (3,-7) as a solution:

y = -1x + b

-7 = -1*3 + b

b = - 4

The equation is therefore   y = -x - 4