Question

In the rectagular prism shown below, GH is parallel to EF. If the equation of GH is 6y-x=2, could the equation of EF be 4=y-1/6x? Explain your reasoning.

Answer 1

Yes

Explanation:

Given

GH:

`-6y - x = 2`

Required

Can EF be

`4 = y - (1)/(6)x`

First, we determine the slope of GH

`-6y - x = 2`

Solve for 6y

`6y = -x - 2`

Solve for y

`y = -(1)/(6)x - (2)/(6)`

`y = -(1)/(6)x - (1)/(3)`

An equation has the form:

`y =mx + b`

Where

`m = slope`

By comparison:

`m = -(1)/(6)`

Next, determine the slope of EF

`4 = y - (1)/(6)x`

Make y the subject

`y = -(1)/(6)x + 4`

The slope is:

`m = -(1)/(6)`

Compare the slopes of both lines.

`m=m = -(1)/(6)`

Since they have the same slopes, then the equation of EF is possible