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.

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Mathematics

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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.

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MrRoyal MrRoyal · Answer 1 · 2025-04-01T02:41:12-04:00

Answer:

Yes

Step-by-step explanation:

Given

GH:

[tex]-6y - x = 2[/tex]

Required

Can EF be

[tex]4 = y - \frac{1}{6}x[/tex]

First, we determine the slope of GH

[tex]-6y - x = 2[/tex]

Solve for 6y

[tex]6y = -x - 2[/tex]

Solve for y

[tex]y = -\frac{1}{6}x - \frac{2}{6}[/tex]

[tex]y = -\frac{1}{6}x - \frac{1}{3}[/tex]

An equation has the form:

[tex]y =mx + b[/tex]

Where

[tex]m = slope[/tex]

By comparison:

[tex]m = -\frac{1}{6}[/tex]

Next, determine the slope of EF

[tex]4 = y - \frac{1}{6}x[/tex]

Make y the subject

[tex]y = -\frac{1}{6}x + 4[/tex]

The slope is:

[tex]m = -\frac{1}{6}[/tex]

Compare the slopes of both lines.

[tex]m=m = -\frac{1}{6}[/tex]

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