Quadrilateral EFGH is on a coordinate plane. Segment FG is on the line 2x − y = −3, and segment EH is on the line 2x − y = 1. Which statement proves how segments FG and EH are related?

- They have the same slope of 2 and are, therefore, parallel.
- They have slopes that are opposite reciprocals of 1 and −1 and are, therefore, perpendicular.
- They have slopes that are opposite reciprocals of 0 and undefined and are, therefore, perpendicular.
- They have the same slope of −1 and are, therefore, parallel.

They have the same slope of 2 and are, therefore, parallel.

Step-by-step explanation:

Given: Equation of FG is and equation of EH is

To find: Relation between segments FG and EH

Solution:

Slope of a line describes its direction and the steepness.

Two lines are said to be parallel if their slopes are equal.

Differentiate with respect to x

where denotes the slope of the line FG

Differentiate with respect to x

where denotes slope of line EH

As , lines are parallel

true

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x