Answer
$y=\dfrac{3}{4}x+5$
Work Step by Step
We have to determine the equation
$$y=mx+b,$$
where
$y$ represents the snow's depth
$x$ represents the snowfall time.
We are given two points on the graph of the line describing the equation: $(4,8)$ and $(6,9.5)$.
$\textbf{First method}$
We will write the equation in point-slope form, then rewrite it in slope-intercept form.
We calculate the slope:
$$m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9.5-8}{6-4}=\dfrac{3}{4}.$$
We determine the point-slope equation using the slope $m$ and one of the points, $(4,8)$:
$$y-y_0=m(x-x_0)$$
$$y-8=\dfrac{3}{4}(x-4)$$
Rewrite the equation in slope-intercept form:
$$y=\dfrac{3}{4}x-3+8$$
$$y=\dfrac{3}{4}x+5.$$
$\textbf{Second method}$
We will calculate the slope of the line, then its $y$-intercept and finally write the equation in slope-intercept form.
We calculate the slope:
$$m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9.5-8}{6-4}=\dfrac{3}{4}.$$
Substitute the slope and the coordinates of one point, for example $(4,8)$, into the slope-intercept form and solve for $b$:
$$\begin{align*}
y&=mx+b\\
8&=\dfrac{3}{4}(4)+b\\
b&=8-3=5.
\end{align*}$$
Substitute $m$ and $b$ into the slope-intercept form:
$$y=\dfrac{3}{4}x+5.$$
