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=(y_2-y_1)/(x_2-x_1) \\ m=(7-(-8))/(3-(-2)) \\ m=(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`