Question

which is the equation for the linear function f in the form f(x) = mx + b that has the given values? f(-2) = - 8, f(3) = 7

Answer 1

The information we have is:

$\begin{gathered} f(-2)=-8 \\ f(3)=7 \end{gathered}$

So we can find that two coordinates are ( -2,-8 ) and ( 3,7 ) so we can use the equation to find the slope so:

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{7-(-8)}{3-(-2)} \\ m=\frac{15}{5} \\ m=3 \end{gathered}$

So the equation now will be:

$y=3x+b$

So we can replace one coordinate to find b so:

$\begin{gathered} 7=3(3)+b \\ 7=9+b \\ 7-9=b \\ -2=b \end{gathered}$

So the final equation is:

$y=3x-2$