Answer
The required values are,\[m=-6\ \text{and}\ b=5\]
Work Step by Step
Put \[x=-3\]in the given function to get the linear equation\[-3m+b=23\].
Put \[x=2\]in the given function to get the linear equation\[2m+b=-7\].
Subtract the obtained equation from both RHS and LHS as follows:
\[\underline{\begin{align}
& -3m+b=23 \\
& -2m-b=+7
\end{align}}\]
\[\begin{align}
& -5m\ \ \ \ \ \ \ =30 \\
& m=-6
\end{align}\]
Put\[m=-6\]in\[-3m+b=23\]to get:
\[\begin{align}
& -3\left( -6 \right)+b=23 \\
& 18+b=23 \\
& b=5
\end{align}\]
To verify put\[m=-6\]and \[b=5\] in\[2m+b=-7\]as follows:
\[\begin{align}
& 2\left( -6 \right)+5=-7 \\
& -12+5=-7 \\
& -7=-7
\end{align}\]
Since RHS\[=\]LHS
Hence verified.
Hence, the\[m=-6\ \text{and}\ b=5\].
