Final answer:
The linear model that relates the number of computers c to the price p is c = -25p + 800.
Step-by-step explanation:
To write a linear model that relates the number of computers c to the price p, we need to find the equation of the line that represents the relationship between these two variables. Since the relationship is said to be linear, we can use the slope-intercept form of a linear equation, which is y = mx + b.
In this case, the number of computers c is the dependent variable (y) and the price p is the independent variable (x). The given information tells us that at a price of $800, 80 computers are sold, and at a price of $550, 100 computers are sold.
To find the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (80, 800) and (100, 550), we can substitute these values into the formula:
m = (550 - 800) / (100 - 80) = -25
Now that we have the slope, we can use one of the points and the slope to find the y-intercept (b) using the formula:
b = y - mx
Using the point (100, 550) and the slope -25:
b = 550 - (-25)(100)
= 800
Therefore, the linear model that relates the number of computers c to the price p is:
c = -25p + 800