Quadrilateral EFGH is on a coordinate plane.Segment GH is on the line 2x+y=2, and segment FE is on the line 2x+y=4. Which statement proves how segments GH and FE are related?A.They have slopes that are opposite reciprocals of 2 and -2 and are , therefore, perpendicular.B. They have the same slope of 2 and are , therefore, parallel.C. They have slopes that are opposite reciprocals of 0 and undefined and are, therefore, perpendicular.D. They have the same slope of -2 and are , therefore, parallel.

Answer: OPTION D.Step-by-step explanation: The equation of the line in Slope-Intercept form is: [tex]y=mx+b[/tex] Where "m" is the slope and "b" is the y-intercept. You know that the segment GH is on this line: [tex]2x+y=2[/tex] Solving for "y", you get: [tex]y=-2x+2[/tex] So you can identify that: [tex]m=-2\\b=2[/tex] The segment FE is on this line: [tex]2x+y=4[/tex] Solving for "y", you get: [tex]y=-2x+4[/tex] Then you can identify that: [tex]m=-2\\b=4[/tex] As you can notice, the lines have the same slope of [tex]-2[/tex]. This means that they are parallel.