To solve the exercise, you can take two ordered pairs from the table, calculate the slope through which these points pass, and then use the point-slope formula to find the equation of the line in its slope-intercept form.
So, you can take for example the points (-5,2) and (3, -14).
The formula for the slope is
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope of the line and} \\ (x_1,y_1),(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex]
In this case, you have
[tex]\begin{gathered} (x_1,y_1)=(-5,2) \\ (x_2,y_2)=(3,-14) \\ m=\frac{-14-2}{3-(-5)} \\ m=\frac{-16}{3+5} \\ m=\frac{-16}{8} \\ m=-2 \end{gathered}[/tex]
Now, using the point-slope formula, you have
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-2_{}=-2(x-(-5)_{}) \\ y-2_{}=-2(x+5_{}) \\ y-2_{}=-2x-10 \\ \text{ Add 2 from both sides of the equation} \\ y-2_{}+2=-2x-10+2 \\ y=-2x-8 \end{gathered}[/tex]
Therefore, the equation that represents the function in the table is
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