Question

Linda found that the cost to get a swimming pool installed in her backyard is a linear function of the pool's area. A swimming pool with an area of 1,500 square feet can be installed for $54,000, whereas the installation of a 700 square foot swimming pool costs $30,000. Make a graph that represents this function and write the equation of the line. Let A represent the pools area and C represent the cost.

Answer 1

Answer:

T he equation of the line is $C = 30A + 9000$

Step-by-step explanation:

If A represents the Area and C represents the cost, then we know that:

For an area $A = 1500$ square feet, the cost is $C = 54000$

If $A = 700$, then, $C = 30000$

Since we know that the cost equation is a function of the area it is a linear relationship so we must find the equation of the line

$C = mA + b$

Where:

m is the slope of the line

b is the intersection with the C axis ..

We already have 2 points:

(700, 30000)

(1500, 54000)

With these points we find the slope using the formula:

$m = \frac{y_2 -y_1}{x_2-x_1}\\\\m = \frac{54000-30000}{1500-700}\\\\m = 30$

So the equation is:

$C = 30A +b$

We find b replacing the point (700, 30000) in the equation

$30000 = 30(700) + b\\\\30000 -21000=b$

$b = 9000$

So

$C = 30A + 9000$

The graph of the linear equation is shown in the attached image