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1 vote
Which statement explains how the lines x + y = 2 and y = x + 4 are related?

A. they are parallel
B. they are perpendicular
C. they are the same line
D. they are not related

User SeekDaSky
by
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2 Answers

2 votes

Answer: B: They are perpendicular

Explanation:

First, you have to convert the equations into y=mx+b form; thankfully, one is already done for us. x+y=2, to convert into y=mx+b form, you have to subtract x. then y=2-x, or in other words, y=-x+2. now that the equations are both in y=mx+b form, we can start graphing them. As I don't have a phone, I will try my best to explain how it is graphed rather than take a picture. For the first equation, y=-x+2, it will start at the height of 2 units. since we can substitute values for x, we can substitute x for 1, and immediately we have to multiply 1 by -1, which is -1. add 2 to -1, and you get 1. so when x increases by 1, y decreases by 1. This trend will continue with different numbers. The second equation, or y=x+4, is pretty straightforward. the y-value starts at a height of 4, and every time the x-value increases by 1, so does the y-value. Now notice how these equations have different meanings, and slopes. this means that they aren't parallel as they don't have the same slope, and they cannot be the same line as they are different equations. This only leaves B or D. When you graph it, you see that the two equations form two lines that cross together and form 4 90-degree angles, which is exactly what perpendicular means. Hope this helps!

User Guyyug
by
6.8k points
4 votes
Answer is B. They are perpendicular

Step by step

Two lines are perpendicular if their slopes are negative reciprocals.

x + y = 2
Change to slope intercept form

y = -x + 2
and
y = x + 4

Slopes are negative reciprocal of each other so your answer is B. They are perpendicular
User Bas H
by
8.0k points