Question

I need to answer this questions but I don't understand

Answer 1

Answer:

The equation that can model the function on the table is;

$y=4x+21$

Explanation:

Given the table in the attached image.

We want to find the equation that models the table.

Using the first two ordered pair on the table;

$\begin{gathered} (x_1,y_1)=(-8,-11) \\ (x_2,y_2)=(-4,5) \end{gathered}$

Recall that the point slope form of lnear equation can be modified to solve for the slope intercept form of the linear equation;

$\begin{gathered} y-y_1=m(x-x_1) \\ m=\frac{y_2-y_1}{x_2-x_1} \\ y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \end{gathered}$

substituting the ordered pair;

$\begin{gathered} y-(-11)_{}=\frac{5-(-11)_{}}{-4_{}-(-8)_{}}(x-(-8)_{}) \\ y+11=\frac{5+11}{-4+8}(x+8) \\ y+11=\frac{16}{4}(x+8) \\ y+11=4(x+8) \\ y+11=4x+32 \\ y=4x+32-11 \\ y=4x+21 \end{gathered}$

Therefore, the equation that can model the table is;

$y=4x+21$