From the given graph, we can note a linear behavior. In order to find the line equation, we need 2 points. One point is (0,0) and the other point is (6,4)
The line equation in slope-intercept form is
[tex]h=md+b[/tex]
Since the slope formula for 2 point is
[tex]m=\frac{h_2-h_1}{d_2-d_1}[/tex]
with
[tex]\begin{gathered} (d_1_{},h_1)=(0,0) \\ (d_2,h_2)=(6,4) \end{gathered}[/tex]
we have that
[tex]\begin{gathered} m=\frac{4-0}{6-0} \\ \text{which gives } \\ m=\frac{4}{6}=\frac{2}{3} \end{gathered}[/tex]
Then, our line equation has the form
[tex]h=\frac{2}{3}d+b[/tex]
and we can find the y-intercept b by replacing one of the 2 points, The "easy" point in this case is (0,0), which gives
[tex]\begin{gathered} 0=\frac{2}{3}(0)+b \\ \text{then} \\ 0=0+b \\ or \\ b=0 \end{gathered}[/tex]
Therefore, the answer is
[tex]h=\frac{2}{3}d[/tex]
which corresponds to the last option from top to bottom
