Question

Please help me ASAP! 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?
A: They have slopes that are opposite reciprocals of 1 and -1 and are, therefore, perpendicular.

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

Answer 1

Hello!

The answer is:

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

Why?

To solve the problem, we must remember that the slope of a line is represented by the coefficient of the linear term (x) or variable.

The coefficient is the number before the variable, for example:

$3X=3*X$

The coefficient of the example is 3.

So, we are given the lines:

First:

$x-y=-3\\\\y=x+3$

We can see that the coefficient of the linear term is equal to 1.

Second:

$x-y=1\\\\y=x-1$

We can see that the coefficient of the linear term is equal to 1.

Hence, we have that both functions have an equal slope of 1, so, the lines are parallel.

The correct option is:

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

Have a nice day!

Note: I have attached a picture for better understanding. The first function is represented by the red line, and the second function is represented by the blue line.