Statistics

Penny recorded the hours she worked as a waitress and how much money she earned in tips. This scatterplot shows her results. Based on the line of best fit, which statement is true? The line of best fit passes through points (2, 20) and (8, 80). Answer choices: - As the number of hours worked increases by 1 hour, the amount of tip money earned increases by $10. - As the number of hours worked increases by 1 hour, the amount of tip money earned increases by $20. - The initial amount of tip money is $2. - The initial amount of tip money is $10.

Step-by-step solution with explanation

Final Answer

As the number of hours worked increases by 1 hour, the amount of tip money earned increases by 10 more in tips per additional hour worked.)

Step-by-step solution

1

Identify two points on the line

and
The problem tells us the line of best fit passes through these two points. The x-value is hours worked and the y-value is tip money earned in dollars.
2

Calculate the slope of the line

Slope = rise over run. We subtract the y-values and divide by the difference in x-values. A slope of 10 means for every 1 hour increase, tips go up by $10.
3

Write the equation in slope-intercept form

We plug in the slope (10) and one point (2, 20) to solve for b, the y-intercept. The y-intercept b = 0 means the initial tip amount is $0, not one of the listed options, so the slope interpretation is key.
4

Interpret the slope as the rate of change

\text{For every } +1 \text{ hour: tips increase by } \$10
The slope of 10 directly tells us the rate. Each additional hour worked earns $10 more in tips. This matches one of the answer choices exactly.
5

Check and eliminate the other answer choices

The initial tip amount (y-intercept) is 2 or 20 per hour choice is also wrong.

Understanding this problem

Learning Insight

The slope of a line of best fit is the rate of change — it tells you how much y changes for each 1-unit increase in x. The y-intercept tells you the starting value when x = 0. These two values together describe the whole linear relationship.

Quick Tip

To find the slope quickly, just divide the change in y by the change in x: (80−20)÷(8−2). If you spot that both coordinates doubled from one point to the other, that's a clue the line passes through the origin (b = 0).

Common Mistake

Students often confuse the slope with the y-intercept and say the initial amount is 10 is the rate of change per hour, not the starting value. Always check which quantity the question is actually asking about.