Maths Question on Linear Function?

Question

A firm is prepared to produce 290 items per week if it can sell at a unit price of $50, iin order to increase revenue, the firm is prepared to increase production to 750 items per week if it can sell them at 70

a) find a linear function for production quantity in terms of price (i.e the supply function)

Can anyone help me on this, i'm stuck

Answer 1

Here's my best shot at it.

Linear, so it takes the form y=mx+b

x= Unit Price

y= Production Quantity

We have two reference points: (50,290) and (70,750)

m=slope, =(750-290) / (70-50)

m=460/20, =23

y=23x+b

Line passes through (50,290)

So 290=23(50)+b

290=1150+b

-860=b

The linear function is y=23x-860