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The equation given is:

\[
y = 5 + 0.5x
\]

where $ y $ represents the cost of getting a car wash and using the vacuum for $ x $ minutes.

### 1. What is the **y-intercept**?

In the equation $ y = 5 + 0.5x $, the **y-intercept** is the constant term, which is 5. This is because when $ x = 0 $, $ y = 5 $. Therefore, the **y-intercept** is 5.

### 2. What does the **y-intercept** represent?

The **y-intercept** represents the starting cost of the car wash, which is the cost when no vacuum time has been used (i.e., $ x = 0 $). In this case, it means that the cost of the car wash alone, without using the vacuum, is $5.

Would you like further details or have any questions? Here are some related questions that can deepen your understanding:

1. How does the slope of 0.5 affect the total cost?
2. What would the cost be after using the vacuum for 10 minutes?
3. If the cost were $8, how many minutes would you have used the vacuum for?
4. How would the graph look if the vacuum rate increased to $1 per minute?
5. What does the slope represent in terms of the relationship between the time and cost?

**Tip:** The **y-intercept** in a linear equation is always where the graph crosses the y-axis, which is when the input (x) equals 0.

What is the y-intercept? What does the y-intercept represent?

Understand how to determine the y-intercept of the linear equation y = 5 + 0.5x and what it represents. This example demonstrates the cost of a car wash starting at $5 with additional charges based on vacuum use. Perfect for students in Grades 7-9 studying algebra.

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