Use slopes to determine if the lines y=−4 and x=−1 are perpendicular.

The lines y=−4 and x=−1 are perpendicular.

Step-by-step explanation:

Given the lines

y=−4

x=−1

The equation y = -4 indicates that the line is horizontal because the value of y remains constant no matter what the value of x is. We also know that the slope of a horizontal line is zero.

In other words, there is no change in y-value i.e. (y₂-y₁) = 0.

Thus, the slope of the horizontal line y = -4 is zero.

Therefore, the slope of y = -4 is: m₁ = 0

The equation x = -1 indicates that the line is vertical because the value of x remains constant no matter what the value of y is. We also know that the slope of a vertical line is undefined or ∞.

In other words, there is no change in x-value i.e. (x₂-x₁) = 0.

Thus, the slope of the vertical line x = -1 is zero.

Therefore, the slope of x = -1 is: m₂ = ∞.

We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line.

As the slope of line y = -4 is: m₁ = 0

Thus, the slope of the the new perpendicular line = m₂ = – 1/m = -1/0 = ∞

Therefore, the lines y=−4 and x=−1 are perpendicular.

ALSO:

From the attached graph, it is clear that:

It is clear that both lines are perpendicular as they are meeting at a right angle.

Therefore, the lines y=−4 and x=−1 are perpendicular.