Question

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

How do these equations compare to line A?

Drag and drop the equations into the boxes to complete the table.

Parallel line A. Perpendicular to line A. Neither parallel nor perpendicular to line A


Y=1/4x+1. Y=4x-8. Y=-4x-3

Please help a person out I'm totally clueless on this

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

Parallel line A :
`y=(1)/(4)x+1`

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

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

Explanation:

The equation of line A is

`y=(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=(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=(1)/(4)x+1`, the slope is 1/4 which is same as slope of line A. So, line
`y=(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* (1)/(4)=1\\eq -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* (1)/(4)=-1`. So, line
`y=-4x-3` perpendicular to line A.