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? A) They have opposite reciprocals slopes of one third and −3 and are, therefore, perpendicular.

B) They have the same slope of negative one third and are, therefore, parallel.

C) They have opposite reciprocal slopes of negative one third and 3 and are, therefore, perpendicular.

D) They have the same slope of 3 and are, therefore, parallel.

D) They have the same slope of 3 and are, therefore, parallel.

Step-by-step explanation:

Given:

Segment FG is on the line 3x − y = −2

Segment EH is on the line 3x − y = −6

Take equation of a line: y = mx + b

Where,

Slope = m

y-intercept = b

Segment FG : 3x - y = -2

Solve for y:

y = 3x + 2

Thus, we have:

Slope = 3

y-intercept = 2

For segment EH: 3x - y = -6

Solve for y:

y = 3x + 6

Thus, we have:

Slope = 3

y-intercept = 6

Since both lines have the same slope of 3, they are parallel.

Option D

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Step-by-step explanation: