Recall from Intermediate Algebra that two non-vertical lines are perpendicular if and only if they have negative reciprocal slopes. That is to say, if one line has slopem1and the other has slopem2thenm1 · m2 = −1.Please note that a horizontal line is perpendicular to a vertical line and vice versa, so we assumem1 ≠ 0andm2 ≠ 0.Below, you are given a line and a point which is not on that line. Find the line perpendicular to the given line which passes through the given point.

Complete Question

The complete question is shown on the first uploaded image

The line is

Step-by-step explanation:

From the question we are told that

The line is

The point is P(0,0 )

Generally the equation for a line is

Now comparing this with the given equation we see that

Generally the slope of the perpendicular to the given line is mathematically evaluated as

=>

=>

Generally from the univesal equation of a line and the given point we have that

y = mx + c at p(0,0) and is

0 = -4 (0 ) + c

=> c = 0

Hence the equation perpendicular to the line given at the point given is

the first option is the answer.