Answer
The required values are,\[m=-4\ \text{and}\ b=3\]
Work Step by Step
The linear function is\[f\left( x \right)=mx+b\]where\[f\left( -2 \right)=11\]and\[f\left( 3 \right)=-9\].
Put \[x=-2\]in the given function to get the linear equation\[-2m+b=11\].Put \[x=3\]in the given function to get the linear equation\[3m+b=-9\].
Subtract the obtained equation from both RHS and LHS as follows:
\[\underline{\begin{align}
& -2m+b=11 \\
& -3m-b=+9
\end{align}}\]
\[\begin{align}
& -5m\ \ \ \ \ \ \ =20 \\
& m=-4
\end{align}\]
Put\[m=-4\]in\[-2m+b=11\]to get:
\[\begin{align}
& -2\left( -4 \right)+b=11 \\
& -8+b=11 \\
& b=3
\end{align}\]
To verify put\[m=-4\]and \[b=3\] in\[3m+b=-9\]as follows:
\[\begin{align}
& 3\left( -4 \right)+3=-9 \\
& -12+3=-9 \\
& -9=-9
\end{align}\]
RHS\[=\]LHS
Hence verified.
Hence, the\[m=-4\ \text{and}\ b=3\].
