A manufacturer of graphing calculators has determined that 11,000 calculators per week will be sold at a price of $90 each. At a price of $80, it is estimated that 17,000 calculators would be sold.

A.) determine a linear function that will predict the number of calculators that would be sold at a given price, x.
B.) use this model to predict the number of calculators that would be sold each week at a price of $60.

To determine a linear function that predicts the number of calculators sold at a given price, we need to find the equation of a straight line that passes through two points: (x₁, y₁) and (x₂, y₂).

Given the information provided, we have two points: (80, 17000) and (90, 11000).

A.) Determining the linear function:
Step 1: Find the slope (m) of the line using the formula: m = (y₂ - y₁) / (x₂ - x₁)
Using (80, 17000) and (90, 11000):
m = (11000 - 17000) / (90 - 80)
= -6000 / 10
= -600

Step 2: Choose one of the points (let's use (80, 17000)) and substitute the values into the equation: y - y₁ = m(x - x₁).
y - 17000 = -600(x - 80)

Simplifying:
y - 17000 = -600x + 48000
y = -600x + 48000 + 17000
y = -600x + 65000

Therefore, the linear function that predicts the number of calculators sold at a given price is:
Number of calculators sold (y) = -600x + 65000.

B.) Using this model to predict the number of calculators sold at a price of $60:
Plug in x = 60 into the linear function:
y = -600(60) + 65000
= -36000 + 65000
= 29000

Therefore, according to the model, the predicted number of calculators that would be sold each week at a price of $60 is 29,000.

You are looking for a fofula of the form

N = a - b P

Where N is the number sold and P is the price. a and b are constants you have to determine from your two data points.

11,000 = a - 90 b
17,000 = a - 80 b
a is easily eliminated as follows:
6000 = 10 b
b = 600

Take it from there.