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The function below shows the cost to attend the fair if you ride r rides.

f(r) = 5 + 1.75r

a. What is the y-intercept, and what does it mean?

b. What is the slope, and what does it mean?

c. If Al spent $19.00 at the fair, how many rides did Al ride?

1 answer

Let's analyze the function given:

\[ f(r) = 5 + 1.75r \]

a. Y-intercept

The y-intercept of a linear function occurs when \( r = 0 \).

To find the y-intercept: \[ f(0) = 5 + 1.75(0) = 5 \]

Interpretation: The y-intercept is 5, which means that if a person does not ride any rides (0 rides), the cost to attend the fair is $5. This could represent the entrance fee or a base cost to enter the fair.

b. Slope

The slope of the function indicates how the cost increases with each additional ride. In the function \( f(r) = 5 + 1.75r \), the slope is 1.75.

Interpretation: The slope of 1.75 means that for each ride a person goes on, the cost increases by $1.75.

c. Finding the number of rides Al rode

If Al spent $19.00 at the fair, we can set up the equation:

\[ f(r) = 19 \] \[ 5 + 1.75r = 19 \]

Now, we can solve for \( r \):

  1. Subtract 5 from both sides: \[ 1.75r = 19 - 5 \] \[ 1.75r = 14 \]

  2. Now divide by 1.75: \[ r = \frac{14}{1.75} \] \[ r = 8 \]

Conclusion: Al rode 8 rides at the fair.