Answer
$D(q)=-0.4q+6.9$
Work Step by Step
The function is $p=S(q)=0.3q+2.7$
with $D(2)=6.1$
which is also $(q_2,p_2)=(2,6.1)$
To find the quantity demanded at a price of $\$4.50$ per watermelon, replace p in the demand function with $4.50$ and solve for q.
$4.50=0.3q+2.7$
$0.3q=1.8$
$q=6$
To find m we use the formula:
$m=\frac{p_2-p_1}{q_2-q_1}=\frac{6.1-4.5}{2-6}=-\frac{4}{5}=-0.4$
Assume that the demand function is linear, we have
$p-p_1=m(q-q_1)$
$D(q)-4.5=-0.4(q-q_1)$
$D(q)-4.5=-0.4q+2.4$
$D(q)=-0.4q+6.9$
