Answer
The values of m and b are $-6$ and $5$ respectively.
Work Step by Step
Let us consider the function $f\left( x \right)=mx+b$.
To solve $f\left( -3 \right),$ put the value of $x=-3$ in the equation.
$m\left( -3 \right)+b=23$
It gives:
$-3m+b=23$ (I)
To solve $f\left( 2 \right),$ put the value of $x=2$ in the equation.
$m\left( 2 \right)+b=-7$
It gives:
$2m+b=-7$ (II)
And subtract equation (II) from equation (I) and get
$\begin{align}
& -3m+b-\left( 2m+b \right)=23-\left( -7 \right) \\
& -3m+b-2m-b=23+7 \\
& -5m=30 \\
& m=-6
\end{align}$
Substitute the value of m in equation (I) and get
$\begin{align}
& -3\left( -6 \right)+b=23 \\
& 18+b=23 \\
& b=23-18 \\
& b=5
\end{align}$
Hence, the values of m and b are -6 and 5 respectively.
