Question

6x + 7y = 3y - 3

Step 2 of 2: Find the equation of the line which passes through the point (-13, -8) and is perpendicular to the given line.
Express your answer in slope-intercept form. Simplify your answer.

Answer 1

y = 2x/3 + 2/3

Explanation:

1. Find the slope of the given line.

y = mx + b

6x + 7y = 3y -3

4y = -6x - 3

y = (-6x-3)/4 = -3x/2 - 3/4

The slope of y = -3/2

The slope of a line perpendicular to the line of 6x + 7y = 3y -3 would be the negative reciprocal of the slope so the slope of the line perpendicular would be -1/(-3/2) = 2/3

The equation would be:

y = 2x/3 + b

Since b is unknown, but a point is known, we plug in x and y values.

-8 = 2*(-13)/3 + b

Then solve for b:

b = 2/3