Question

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.

Answer 1

Answer:

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

Step-by-step explanation:

Given: Equation of FG is $2x-y=-3$ and equation of EH is $2x-y=1$

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.

$2x-y=-3$

Differentiate with respect to x

$2-y'=0\\y'=m_1=2$

where $m_1$ denotes the slope of the line FG

$2x-y=1$

Differentiate with respect to x

$2-y'=0\\y'=m_2=2$

where $m_2$ denotes slope of line EH

As $m_1=m_2=2$, lines are parallel