Question

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.

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The line is $y = -4 x$

Step-by-step explanation:

From the question we are told that

The line is $y = \frac{1}{4} x + 8$

The point is P(0,0 )

Generally the equation for a line is $yn = mx + c$

Now comparing this with the given equation we see that

$m =\frac{1}{4} = slope$

$C =8 = intercept$

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

$m_1 = - \frac{1}{m}$

=> $m_1 = - \frac{1}{ \frac{1}{4}}$

=> $m_1 = -4$

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

y = mx + c at p(0,0) and $m_1 = -4$ is

0 = -4 (0 ) + c

=> c = 0

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

$y = -4 x$