Question

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

A) They are perpendicular lines.
B) They are parallel lines.
C) They intersect at a right angle.
D) They do not have a clear geometric relationship.

Answer 1

The lines x + y = 2 and y = x + 4 are perpendicular to each other.

Step-by-step explanation:

The two lines x + y = 2 and y = x + 4 have a clear geometric relationship. To determine the relationship, we can rewrite both equations in slope-intercept form, which is y = mx + b, where m represents the slope of the line.

By rearranging the equations, we get y = -x + 2 and y = x + 4.

Comparing the slopes, we see that one line has a slope of -1 and the other line has a slope of 1. Since the slopes are negative reciprocals of each other, the two lines are perpendicular to each other.

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