Answer
$D(q)=-0.35q+9$
Work Step by Step
The function is $p=S(q)=0.25q+3.6$
with $D(4)=7.6$
which is also $(q_2,p_2)=(4,7.6)$
To find the quantity demanded at a price of $\$5.85$ per watermelon, replace p in the demand function with $5.85$ and solve for q.
$5.85=0.25q+3.6$
$0.25q=2.25$
$q=9$
To find m we use the formula:
$m=\frac{p_2-p_1}{q_2-q_1}=\frac{7.6-5.85}{4-9}=-\frac{7}{20}=-0.35$
Assume that the demand function is linear, we have
$p-p_1=m(q-q_1)$
$D(q)-5.85=-0.35(q-q_1)$
$D(q)-5.85=-0.35q+3.15$
$D(q)=-0.35q+9$
