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

Explanation:

Step1: Find the slope of the line

For the line \(2x - y=-3\), rewrite it in slope - intercept form \(y = mx + b\) (where \(m\) is the slope).

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The slope of the line \(2x - y=-3\) (segment \(FG\)) is \(m_1 = 2\).
For the line \(2x - y=1\), rewrite it in slope - intercept form \(y=mx + b\).

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The slope of the line \(2x - y = 1\) (segment \(EH\)) is \(m_2=2\).

Step2: Use the parallel line condition

Two lines \(y = m_1x + b_1\) and \(y=m_2x + b_2\) are parallel if \(m_1=m_2\). Since \(m_1 = 2\) and \(m_2 = 2\), segments \(FG\) and \(EH\) are parallel.

Answer:

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