Question

Line A is represented by the equation y=1/4x+8

Answer 1

This comes from y=mx+b, where m is slope and b is the y-intercept.

Parallel means they will never meet.

Perpendictular means they meet at a right angle.

Neither, i assume, means they meet, but not at a right angle.

First one, y=1/4x+1 has the same slope but different intercepts so it is parallel.

Second, y=4x-8, has to be neither because they do meet (somewhere in the third quadrant) , but it's not at a right angle

And Third, y=-4x-3, this one is also neither because they meet (again not at a right angle) in quadrant 2.

I Hope This Answered Your Question!!

Answer 2

Answer:

Parallel line A : $y=\frac{1}{4}x+1$

Perpendicular to line A : $y=-4x-3$

Neither parallel nor perpendicular to line A : $y=4x-8$

Step-by-step explanation:

The equation of line A is

$y=\frac{1}{4}x+8$       ... (1)

The slope intercept form of a line is

$y=mx+b$               .... (2)

where, m is slope and b is y-intercept.

From (1) and (2) we get

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

It means the slope of line A is 1/4.

The slope of parallel lines are same and the product of slopes of two perpendicular lines is -1.

In equation $y=\frac{1}{4}x+1$, the slope is 1/4 which is same as slope of line A. So, line $y=\frac{1}{4}x+1$ is parallel to line A.

In equation $y=4x-8$, the slope is 4 which not equal to slope of line A and $4\times \frac{1}{4}=1\neq -1$. So, line $y=4x-8$ is neither parallel nor perpendicular to line A.

In equation $y=-4x-3$, the slope is -4 which is not equal to the slope of line A and $-4\times \frac{1}{4}=-1$. So, line $y=-4x-3$ perpendicular to line A.