Determine the slope of a line perpendicular to the line with equation 6x-4y = 30

Start by putting it in slope intercept form.

6x - 4y = 30

6x - 30 = 4y

(6/4) x - 30/4 = y

simplify

(3/2) x - 15/2 = y

A perpendicular line will have a reversed slope. Take the negative reciprocal (flip it over, make negative).

slope of perpendicular line: - 2/3

6x - 4y = 30

-4y = - 6x + 30

y = 3/2x - 15/2 ... slope here is 3/2. A perpendicular line will have a negative reciprocal slope. All that means is flip the slope and change the sign. So ur perpendicular line will have a slope of - 2/3 (see how I flipped 3/2 making it 2/3 ... and then changed the sign, making it - 2/3)

answer : perpendicular line will have a slope of - 2/3.