12. Write the equation in slope-intercept form of the line that passes through (4, −5) and is perpendicular to the graph of y = 4x + 12.

Answer 1

Hello Zr,

When two lines are perpendicular, the product of their slopes equals -1.

so (slope 1) * (slope 2) = -1

---> 4 * slope 2 = -1 ---> slope 2 = -1/4

So the perpendicular line has an equation of the form: y = (-1/4)*x + b

To find b, you would plug (4, -5) in that equation since the line goes through that point:

-5 = (-1/4)*4 + b ----> -5 = -1+b ---> b = -4

Therefore, the equation you are looking for is: y = (-1/4)*x -4

Cheers.