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.

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luisejr77 luisejr77 · Answer 1 · 2019-04-11T07:34:48+02:00

Answer:

T he equation of the line is [tex]C = 30A + 9000[/tex]

Step-by-step explanation:

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

For an area [tex]A = 1500[/tex] square feet, the cost is [tex]C = 54000[/tex]

If [tex]A = 700[/tex], then, [tex]C = 30000[/tex]

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

[tex]C = mA + b[/tex]

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:

[tex]m = \frac{y_2 -y_1}{x_2-x_1}\\\\m = \frac{54000-30000}{1500-700}\\\\m = 30[/tex]

So the equation is:

[tex]C = 30A +b[/tex]

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

[tex]30000 = 30(700) + b\\\\30000 -21000=b[/tex]

[tex]b = 9000[/tex]

So

[tex]C = 30A + 9000[/tex]

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