Solution:

We are tasked with using the given equation for the line of best fit to predict the hourly wage for a person who has worked 12 years.

The equation for the line of best fit is:
$y = \frac{3}{4}x + 8$
Where:

• $y$ is the hourly wage in dollars,
• $x$ is the number of years worked.

To find the hourly wage for 12 years, substitute $x = 12$ into the equation.

Step 1: Substitute $x = 12$ into the equation

$y = \frac{3}{4}(12) + 8$

Step 2: Simplify the multiplication

$\frac{3}{4} \times 12 = \frac{36}{4} = 9$

Step 3: Add the result to 8

$y = 9 + 8 = 17$

Final Answer:

The predicted hourly wage for a person who has worked 12 years is $17 per hour.

Do you have any further questions or want additional details about this process?

Related Questions:

1. How is the slope of the line ($\frac{3}{4}$) interpreted in this context?
2. How does increasing the number of years by 1 affect the hourly wage based on this equation?
3. What is the significance of the y-intercept ($8$) in this scenario?
4. How can we determine whether the line of best fit is accurate for predicting hourly wages?
5. What is another way to verify that $y = 17$ is a reasonable prediction for 12 years of work?

Tip:

When working with equations of lines, always verify that units (e.g., years, dollars) are consistent and clearly labeled to avoid confusion.