Quadrilateral WXYZ is on a coordinate plane. Segment YZ is on the line x+y=7, and segment XW is on the line x+y=3. Which statement proves how segments YZ and XW 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

Question

Mathematics

Jair Hatfield

4 February, 07:28

Quadrilateral WXYZ is on a coordinate plane. Segment YZ is on the line x+y=7, and segment XW is on the line x+y=3. Which statement proves how segments YZ and XW 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

+3

Answers (1)

Know the Answer?

Kira Huff · Answer 1

D. They have the same slope of - 1 and are therefore parallel

Step-by-step explanation:

In the linear equation ...

ax + by = c

the slope of the line is m = - a/b. For the given equations, the slopes are ...

x+y = 7 ⇒ m = - 1/1 = - 1

x+y = 3 ⇒ m = - 1/1 = - 1

The slopes are the same, and both slopes are - 1, so the lines are parallel.