Question

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

Answer 1

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

`y=4x+21`

Step-by-step 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=(y_2-y_1)/(x_2-x_1) \\ y-y_1=(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=(5+11)/(-4+8)(x+8) \\ y+11=(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`