Answer: The price per unit is $48, when 30 units are demanded.
Step-by-step explanation:
Since we have given that
At price of $12 per unit, the number of units demanded = 40 units
At price of $18 per unit, the number of units demanded = 25 units.
So, the coordinates would be
(40,12) and (25,18)
As we know that x- axis denoted the quantity demanded.
y-axis denoted the price per unit.
So, the slope would be
![m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{18-12}{25-40}\\\\m=\dfrac{-6}{15}\\\\m=\dfrac{-2}{5}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%5C%5C%5C%5Cm%3D%5Cdfrac%7B18-12%7D%7B25-40%7D%5C%5C%5C%5Cm%3D%5Cdfrac%7B-6%7D%7B15%7D%5C%5C%5C%5Cm%3D%5Cdfrac%7B-2%7D%7B5%7D)
So, the equation would be
![y-y_1=m(x-x_1)\\\\y-12=\dfrac{-2}{5}(x-40)\\\\5(y-12)=-2(x-40)\\\\5y-60=-2x+80\\\\5y+2x=80+60\\\\5y+2x=140](https://tex.z-dn.net/?f=y-y_1%3Dm%28x-x_1%29%5C%5C%5C%5Cy-12%3D%5Cdfrac%7B-2%7D%7B5%7D%28x-40%29%5C%5C%5C%5C5%28y-12%29%3D-2%28x-40%29%5C%5C%5C%5C5y-60%3D-2x%2B80%5C%5C%5C%5C5y%2B2x%3D80%2B60%5C%5C%5C%5C5y%2B2x%3D140)
So, if 30 units are demanded, the price per unit would be
![5y=140+2x\\\\5y=140+2\times 30\\\\5y=140+60\\\\5y=240\\\\y=\dfrac{240}{5}\\\\y=\$48](https://tex.z-dn.net/?f=5y%3D140%2B2x%5C%5C%5C%5C5y%3D140%2B2%5Ctimes%2030%5C%5C%5C%5C5y%3D140%2B60%5C%5C%5C%5C5y%3D240%5C%5C%5C%5Cy%3D%5Cdfrac%7B240%7D%7B5%7D%5C%5C%5C%5Cy%3D%5C%2448)
Hence, the price per unit is $48, when 30 units are demanded.