Answer
The values of m and b are $-4$ and $3$ respectively.
Work Step by Step
We have the function $f\left( x \right)=mx+b$.
To solve $f\left( -2 \right),$ put the value of $x=-2$ in the equation:
$m\left( -2 \right)+b=11$
It gives:
$-2m+b=11$ (I)
Then solve $f\left( 3 \right),$ put the value of $x=3$ in the equation:
$m\left( 3 \right)+b=-9$
It gives:
$3m+b=-9$ (II)
And subtract the equation (II) from equation (I):
$\begin{align}
& -2m+b-\left( 3m+b \right)=11-\left( -9 \right) \\
& -2m+b-3m-b=11+9 \\
& -5m=20 \\
& m=-4
\end{align}$
Substitute the value of m in equation (I) and get:
$\begin{align}
& -2\left( -4 \right)+b=11 \\
& 8+b=11 \\
& b=11-8 \\
& b=3
\end{align}$
Hence, the values of m and b are -4 and 3 respectively.
