Considering the values of their slopes, it is found that the linear functions are perpendicular.
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
The slope determines if the lines are parallel, perpendicular, or neither, as follows:
- If they are equal, the lines are parallel.
- If their multiplication is of -1, they are perpendicular.
- Otherwise, they are neither.
For the line through points (-3,-1) and (1,-9), the slope is:
m = (-9 + 1)/(1 + 3) = -2
For the line through points (1,4) and (5,6), the slope is:
m = (6 - 4)/(5 - 1) = 2/4 = 0.5.
-2 x 0.5 = -1, hence they are perpendicular.
More can be learned about linear functions at https://brainly.com/question/24808124
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