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

Question

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?

Answer 1

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.