Question

Find k so that the line through (3,-1) and (k,2) is perpendicular to 2x+3y=6

Answer 1

The slopes of perpendicular lines are negative reciprocals.
That means that the product of the slopes of perpendicular lines is -1.

First, we find the slope of the given line.
2x + 3y = 6
3y = -2x + 6
y = (-2/3)x + 6
The slope of the given line is -2/3.

The slope we need is 3/2.
Now we set the slope of the line through the two given points equal to 2/3, and we solve for k.

(-1 - 2)/(3 - k) = 3/2
-3/(3 - k) = 3/2
3/(k - 3) = 3/2
k - 3 = 2
k = 5