Use slopes to determine if the lines y=−4 and x=−1 are perpendicular.
2 answers:
Answer:
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:
- The red line is representing y = -4
- The blue line is representing x = -1
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.
You might be interested in
Answer:
(0, -3)
Step-by-step explanation:
The solution to the system of equations is the point at which they intersect. The problem statement tells you that point is (x, y) = (0, -3).
__
Often, for a system defined using functional notation, we don't care about the value of the function. We only care about the value of x where the functions have the same value. That is ...
the solution to f(x) = g(x) is x = 0.
