Answer
The linear function is $f(x)=-6$.
Work Step by Step
Rewrite as shown below.
$f(-1)=-6$ as $(-1,-6)$
and $f(4)=-6$ as $(4,-6)$
Let $(x_1,y_1)=(-1,-6)$ and $(x_2,y_2)=(4,-6)$.
Slope
$\Rightarrow m =\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m =\frac{-6-(-6)}{4-(-1)}$
Simplify.
$\Rightarrow m =\frac{-6+6}{4+1}$
$\Rightarrow m =\frac{0}{5}$
$\Rightarrow m =0$
The point-slope form.
$\Rightarrow y-y_1=m(x-x_1)$
Substitute all the values.
$\Rightarrow y-(-6)=0(x-(-1))$
Simplify.
$\Rightarrow y+6=0(x+1)$
$\Rightarrow y+6=0$
Subtract $6$ from each side.
$\Rightarrow y+6-6=0-6$
Simplify.
$\Rightarrow y=-6$
Hence, the linear function is $f(x)=-6$.
