What is the equation of the line that is perpendicular to y = 3x - 7 and goes through the point (4, -6). (Answer in slope-intercept form, please.)

Answer 1

Hey Isabela!

We want the perpendicular slope to the line y = 3x - 7. The slope of a line perpendicular to m=3 (the slope of the line in the given equation) is the negative reciprocal of m=3. So in this case we are looking for the slope

-1/m = -1/3

Then we put the point into "point slope form" and then solve for y to put it in slope intercept form.

y - (-6) = -1/3 * (x-4)

y+6 = -x/3 +4/3 distribute and simplify

y = -x/3 +4/3 -6 subtract 6 from both sides

y = -x/3 -14/3 combine constants ( 6 = 18/3 ). Solved

y = -x/3 -14/3 is the line perpendicular to y = 3x - 7 and goes through the point (4,-6)

I hope this helps

-Pete