Question

Jamie says that the pair of lines, y=−4x+4, are perpendicular lines. Natasha says those same lines are parallel. Determine who, if anyone, is correct and explain your thinking.

a) Jamie is correct; the lines are perpendicular because their slopes are negative reciprocals of each other.
b) Natasha is correct; the lines are parallel because they have the same slope.
c) Both Jamie and Natasha are incorrect; the lines are neither perpendicular nor parallel.
d) Both Jamie and Natasha are correct, and it depends on the context of the problem.

Answer 1

The lines y=−4x+4 are parallel because they have the same slope.

Step-by-step explanation:

To determine whether the lines y=-4x+4 are perpendicular or parallel, we need to compare their slopes.

A line in the form y=mx+b has a slope of m.

So, the slope of the given line is -4.

Two lines are perpendicular if and only if their slopes are negative reciprocals of each other.

The negative reciprocal of -4 is 1/4, which is not equal to the slope of the given line. Therefore, the lines y=-4x+4 are not perpendicular.

Since the slopes are not negative reciprocals, the lines cannot be perpendicular. So, Natasha is correct; the lines y=-4x+4 are parallel because they have the same slope.