The scatter plot below shows data regarding the number of years worked and the average hourly wage for a job y=3/4x+8 A reasonable equation for the line of best fit is

Question

, What does the slope represent in this situation?

Question 5 options:

The hourly pay increases by $8 for every year of experience

The hourly pay increases by $3 for every 4 years of experience

The hourly pay increases by $3 for every year of experience

The hourly pay increases by $4 for every 3 years of experience

Answer 1

The given equation of the line is \(y = \frac{3}{4}x + 8\). In this equation, \(y\) represents the average hourly wage, and \(x\) represents the number of years worked.

The slope of the equation, which is \(\frac{3}{4}\), indicates the change in \(y\) (average hourly wage) for a one unit increase in \(x\) (years of experience).

To interpret the slope \(\frac{3}{4}\):

• The slope of \(\frac{3}{4}\) means that for every year of experience (every 1 unit increase in \(x\)), the average hourly pay increases by \(\frac{3}{4}\) dollars (or $0.75).

Looking at the options provided:

• "The hourly pay increases by $8 for every year of experience" (incorrect)
• "The hourly pay increases by $3 for every 4 years of experience" (this is correct: moving 4 years multiplies the slope by 4, giving $3)
• "The hourly pay increases by $3 for every year of experience" (incorrect)
• "The hourly pay increases by $4 for every 3 years of experience" (incorrect)

The correct interpretation of the slope in the context of the question is: The hourly pay increases by $3 for every 4 years of experience.