Quadrilateral EFGH is on a coordinate plane. Segment FG is on the line 3x − y = −2, and segment EH is on the 3x − y = −6. Which statement proves how segments FG and EH are related?

the slope of both lines are the same.

Step-by-step explanation:

Given the following segment of the Quadrilateral EFGH on a coordinate  Segment FG is on the line 3x − y = −2,

segment EH is on the 3x − y = −6.

To determine their relationship, we can find the slope of the lines

For line FG: 3x - y = -2

Rewrite in standard form y = mx+c

-y = -3x - 2

Multiply through by-1

y = 3x + 2

Compare

mx = 3x

m = 3

The slope of the line segment FG is 3

For line EH: 3x - y = -6

Rewrite in standard form y = mx+c

-y = -3x - 6

Multiply through by-1

y = 3x + 6

Compare

mx = 3x

m = 3

The slope of the line segment EH is 3

Hence the statement that proves their relationship is that the slope of both lines are the same.

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