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8 days ago

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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 p

ool 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.

1 answer:

lawyer [12K]8 days ago

3 0

Answer:

The equation for the line is $C = 30A + 9000$

Step-by-step explanation:

Let A denote Area and C stand for Cost, we can deduce that:

For an area of $A = 1500$ square feet, the cost amounts to $C = 54000$

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

Since the cost equation represents a function of area, this establishes a linear connection, necessitating the formulation of the line's equation.

$C = mA + b$

Where:

m denotes the slope of the line

b indicates the intercept with the C axis..

We possess two coordinates:

(700, 30000)

(1500, 54000)

Using these points, we calculate the slope via the formula:

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

Consequently, the equation concludes with:

$C = 30A +b$

To find b, we substitute the point (700, 30000) into the equation

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

$b = 9000$

Thus

$C = 30A + 9000$

The linear equation's graph is depicted in the provided image

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