The linear function [tex]f[/tex] with [tex]f(0) = 3[/tex] and [tex]f(-6) = 3[/tex] is [tex]y = 3[/tex].
Given two distinct points on cartesian plane, we can determine the linear function associated to those points as follows:
[tex]y = m\cdot x + b[/tex] (1)
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] (2)
[tex]b = y_{1}-m\cdot x_{1}[/tex] (3)
If we know that [tex]f(0) = 3[/tex] and [tex]f(-6) = 3[/tex], then we have the linear function below:
[tex]m = \frac{3-3}{0-(-6)}[/tex]
[tex]m = 0[/tex]
[tex]b = 3 - 0\cdot (0)[/tex]
[tex]b = 3[/tex]
The linear function [tex]f[/tex] with [tex]f(0) = 3[/tex] and [tex]f(-6) = 3[/tex] is [tex]y = 3[/tex].
We kindly invite to check this question on linear functions: https://brainly.com/question/19137465
