Geometry math question no guessing and show work

first lets normalize the equation into y=... form. We can do this by dividing all by 4:

y=(5/4)x - 2

5/4 is the gradient of this line. The perpendicular line will have the negative reciprocal gradient, ie., -4/5, so we're looking for a value of -4/5 in front of the x.

That's only answer B. But it has to go through (-5,4). If you fill in -5, you get -5*-4/5 = +4. So y=(-4/5)x is indeed the correct answer.

can you give me more detail on this! ?

step-by-step explanation: