Question

1. a local swimming pool has a membership fee to use its facilities. there is an additional cost for each time you use the pool. the graph shows the total cost of using the swimming pool depending on how many times you visited the pool.

a. what is the y - intercept? what is its meaning in the context of this situation?

b. what is the slope? what is its meaning in the context of this situation?

c. what is the equation of the line in slope - intercept form?

d. after how many visits would you have spent a total of $210?

Explanation:

Step1: Find the y - intercept

The y - intercept is the value of \(y\) when \(x = 0\). Looking at the graph, when \(x=0\) (no visits), \(y = 40\). In the context of the situation, this is the membership fee (the cost when you use the pool \(0\) times).

Step2: Calculate the slope

The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((0,40)\) and \((10,90)\). Then \(m=\frac{90 - 40}{10-0}=\frac{50}{10}=5\). In the context, the slope represents the additional cost per visit.

Step3: Write the equation in slope - intercept form

The slope - intercept form is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. Substituting \(m = 5\) and \(b=40\), we get \(y = 5x+40\).

Step4: Solve for \(x\) when \(y = 210\)

Substitute \(y = 210\) into the equation \(y=5x + 40\).

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Answer:

a. The y - intercept is \(40\). It is the membership fee.
b. The slope is \(5\). It is the additional cost per visit.
c. The equation is \(y = 5x+40\).
d. After \(34\) visits.