Question

quadrilateral wxyz is on a coordinate plane. segment xy is on the line $x - y = -3$, and segment wz is on the line $x - y = 1$. which statement proves how segments xy and wz are related?

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

Explanation:

Step1: Rewrite lines to slope-intercept form

For line $x-y=-3$:
Rearrange to $y = x + 3$
For line $x-y=1$:
Rearrange to $y = x - 1$

Step2: Identify slopes of the lines

Slope of $y=x+3$ is $m_1=1$
Slope of $y=x-1$ is $m_2=1$

Step3: Relate slopes to line relationship

Lines with equal slopes are parallel.

Answer:

B. They have the same slope of 1 and are, therefore, parallel.