Science:Math Exam Resources/Courses/MATH100 C/December 2024/Question 11 (a)/Solution 1

Assume the demand $x$ is linear in price $p$, so $x(p)$ is a line passing through the points $(150,50)$ and $(140,55)$.

Compute the slope: $$m=\frac{55-50}{140-150}=\frac{5}{-10}=-\frac{1}{2}.$$

Using point-slope form with the point $(150,50)$: $$x-50=-\frac{1}{2}(p-150).$$

Simplifying: $$x=-\frac{1}{2}p+75+50=-\frac{1}{2}p+125.$$

Thus, the demand function is $$x(p)=-\frac{1}{2}p+125.$$