John L. answered • 10/07/19

Certified biology teacher specializing in bio and SAT/GRE prep

First you find the slope of the given line. The formula for slope for line in standard form (ax + by = c) is -a/b, so for this line the slope is -3/2.

A perpendicular line's slope is the negative reciprocal of the original line's slope. So the new line will have a slope of 2/3.

Now we can use the given point and the slope to calculate the y-intercept. Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We sub in the given point to yield:

8 = (2/3)(3) + b

8 = 6 + b

b = 2

The line that is perpendicular to 3x + 2y = 10 and goes through point (3,8) is: y = (2/3)x + 6

Standard form answer: -2x + 3y = 18