The linear function [tex]f[/tex] with [tex]f(-10) = 4[/tex] and [tex]f(-2) = 4[/tex] is [tex]y = 4[/tex].
Linear functions are characterized by slope and intercept. Given two distinct points on cartesian plane, we can obtain these two characteristics by means of the following formulas:
[tex]y = m\cdot x + b[/tex] (1)
Slope
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (2)
Intercept
[tex]b = y_{1}-m_{1}\cdot x_{1}[/tex] (3)
If we know that [tex]f(-10) = 4[/tex] and [tex]f(-2) = 4[/tex], then the linear equation is:
[tex]m = \frac{4-4}{-2 - (-10)}[/tex]
[tex]m = 0[/tex]
[tex]b = 4 - 0\cdot (-2)[/tex]
[tex]b = 4[/tex]
Then, the linear function [tex]f[/tex] with [tex]f(-10) = 4[/tex] and [tex]f(-2) = 4[/tex] is [tex]y = 4[/tex].
We kindly invite to check this question on linear functions: https://brainly.com/question/3400735
