Point-Slope equations

[LWilliams-disab]

Suppose that suppliers are willing to sell 5.0 million lb of coffee at a price of $8 per pound and 7.0 million lb at $9 per pound

Find a linear function that expresses the amount suppliers are willing to sell as a function of the price per pound.

Use the function of part (a) to predict how much suppliers are willing to sell at a price of $6 per pound.

[TKHunny]

Suppose that suppliers are willing to sell 5.0 million lb of coffee at a price of $8 per pound and 7.0 million lb at $9 per pound

Find a linear function that expresses the amount suppliers are willing to sell as a function of the price per pound.

Use the function of part (a) to predict how much suppliers are willing to sell at a price of $6 per pound.

Million Pounds(MMlbs) = Function of Price(dollars)
MMlbs = m(dollars)+b

Point: $8 leads to 5.0 MMlbs

Slope: (Change in MMlbs)/(Change in dollars)
Slope: (7.0 - 5.0) / (9 - 😎 = 2/1 = 2

MMlbs = m(dollars)+b

Add the slope:

MMlbs = (2)(dollars)+b

Add the point

5.0 = 2 (8) + b = 16+b

Solve for b (subtract 16)

-11=b

Equation:

MMlbs = (2)(dollars) - 11

Check Both Points:

2(8)-11 = 16-11 = 5 Check.
2(9)-11 = 18-11 = 7 Check.

Predict 6

2(6)-11 = 12-11 = 1 Ouch! Time to apply for subsidies.