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)?
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Answer 1

y=x

Explanation:

slope intercept form:

y= mx +c, where m is the gradient and c is the y-intercept.

Let's rewrite the given equation in the form of y=mx+c, so that we can determine the gradient of the line.

y-4= x-6

y= x -6 +4

y= x -2

Thus, the gradient of the given line is 1.

the product of the gradients of perpendicular lines is -1.

(gradient of line)(1)= -1

gradient of line= 1

Thus, m=1.

y= 1x +c

y= x +c

To find c, substitute a coordinate.

When x= -2, y= -2,

-2= -2 +c

c= -2 +2

c=0.

Thus the equation of the line is y=x.