Answer
The data in the table can be modeled by a linear equation.
The linear equation is $y=-3x+7$.
Work Step by Step
The rate of change for consecutive data pairs in the table.
$\Rightarrow \frac{10-16}{-1-(-3)}=\frac{-6}{-1+3}=-\frac{6}{2}=-3$
$\Rightarrow \frac{4-10}{1-(-1)}=\frac{-6}{1+1}=-\frac{6}{2}=-3$
$\Rightarrow \frac{-2-4}{3-1}=-\frac{6}{2}=-3$
$\Rightarrow \frac{-8-(-2)}{5-3}=\frac{-8+2}{2}=-\frac{6}{2}=-3$
Because the rate of change is constant, the data in the table can be modeled by a linear equation.
Slope is $m=-3$
Use the point $(x_1,y_1)=(1,4)$
The point-slope form is
$\Rightarrow y-y_1=m(x-x_1)$
Substitute $-3$ for $m,1$ for $x_1$ and $4$ for $y_1$.
$\Rightarrow y-4=-3(x-1)$
Use distributive property.
$\Rightarrow y-4=-3x+3$
Add $4$ to each side.
$\Rightarrow y=-3x+7$
