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

Answer:

Yes

Step-by-step explanation:

Given

GH:

$-6y - x = 2$

Required

Can EF be

$4 = y - \frac{1}{6}x$

First, we determine the slope of GH

$-6y - x = 2$

Solve for 6y

$6y = -x - 2$

Solve for y

$y = -\frac{1}{6}x - \frac{2}{6}$

$y = -\frac{1}{6}x - \frac{1}{3}$

An equation has the form:

$y =mx + b$

Where

$m = slope$

By comparison:

$m = -\frac{1}{6}$

Next, determine the slope of EF

$4 = y - \frac{1}{6}x$

Make y the subject

$y = -\frac{1}{6}x + 4$

The slope is:

$m = -\frac{1}{6}$

Compare the slopes of both lines.

$m=m = -\frac{1}{6}$

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