Answer
(a) $F=\frac{9}{5}C+32$
(b) $86^{\circ}$ Fahrenheit
Work Step by Step
(a.) The given function is
$\Rightarrow F=mC+b$
This is the standard slope-intercept form,
where $m$ is the slope and $b$ is the $F-$ intercept..
We have two points in the given graph.
The first point is $=(0,32)$, therefore the $F-$ intercept is $b=32$.
The second point is $(100,212)$.
The slope of the line is $m=\frac{change \; in\; F}{change \; in\; C}$
$m=\frac{212-32}{100-0}$
$m=\frac{180}{100}$
$m=\frac{9}{5}$
Plug all values into the given function.
$\Rightarrow F=\frac{9}{5}C+32$.... (1)
(b.) Plug $C=30^{\circ}$ in equation (1).
$\Rightarrow F=\frac{9}{5}(30)+32$
$\Rightarrow F=54+32$
$\Rightarrow F=86^{\circ}$
