3x – 2y = 24

-2y = -3x + 24

y = (3/2)x – 12

The slope, then is 3/2.

The perpendicular slope is the negative reciprcal of 3/2, which is -2/3.

Now find the x-intercept. This is the point (a, 0). So plug this into the equation and solve for a.

3a – 2*0 = 24

3a = 24

a = 8

So the line passes through the point (8, 0)

Now use the point-slope form of an equation of a line:

y – y1 = m(x – x1), where x1 = 8 and y1 = 0 — the coordinates of the point we solved for that it passes through.

y – 0 = (-2/3)(x – 8)

Now get it into whatever form of the equation you are looking for:

y = (-2/3)x + 16/3

3y = -2x + 16

2x + 3y = 16

I hope this helps!

3x-2y=24

-2y=-3x+24

y=1.5x-12

When a line intersects, the slope has the opposite sign.

y=-1.5x-12

(Here, you’ore assuming that 0,-12 is the coordinate point since you aren’t given another point)