Answer
\[F=\frac{9}{5}C+32\].
Work Step by Step
The graph of the provided equation contains the point\[\left( 0,32 \right)\]. Water freezes at \[0{}^\circ C\]or at\[32{}^\circ F\].
The line also contain the point\[\left( 100,212 \right)\]: Water boils at \[100{}^\circ C\] or at \[212{}^\circ F\].
The slope of the line by the points\[\left( 0,32 \right)\]and \[\left( 100,212 \right)\]is calculated as;
\[\begin{align}
& m=\frac{\text{change in }y}{\text{change in }x} \\
& =\frac{212-32}{100-0} \\
& =\frac{180}{100} \\
& =\frac{9}{5}
\end{align}\]
Hence, the slope is\[\frac{9}{5}\]and the y-intercept, b is 32.
By the formula, \[F=mC+b\]
\[F=\frac{9}{5}C+32\]
Hence, the required linear equation is\[F=\frac{9}{5}C+32\].
