Answer
$y=\frac{4}{3}x-\frac{20}{3}$
Work Step by Step
Let's note the triangle $ABC$ and its vertices:
$$A(8,4), B(0,0), C(10,0)$$
First we determine the coordinates of the point $M$:
$$x_M=\dfrac{x_B+x_C}{2}=\dfrac{0+10}{2}=5.$$
$$y_M=\dfrac{y_B+y_C}{2}=\dfrac{0+0}{2}=0.$$
So the point $M$ has the coordinates $M(5,0)$.
Now we calculate the slope of the line passing through $A$ and $M$ (the median from $A$):
$$m=\dfrac{y_M-y_A}{x_M-x_A}=\dfrac{0-4}{5-8}=\dfrac{4}{3}.$$
Finally we write the point-slope equation of the median $AM$ and rewrite it in slope-intercept form:
$$\begin{align*}
y-y_M&=m(x-x_M)\\
y-0&=\dfrac{4}{3}(x-5)\\
y&=\dfrac{4}{3}x-\dfrac{20}{3}.
\end{align*}$$
