Creating Equations for Lines of Fit

Mr. Weaver introduces eighth-grade students to the concept of lines of fit, teaching them how to create equations from scatter plots using slope and y-intercept. Through examples, students learn to interpret these equations and make predictions about data, such as the relationship between piano practice and mistakes or advertising spend and sales. The lesson emphasizes understanding the limitations of predictions and encourages students to check their understanding through interactive exercises.

What is the main goal of this lesson?

• To learn how to draw scatter plots

• To find the equation for a line that fits the data and use it to predict values

• To understand the concept of slope

• To learn about different types of graphs

When finding the slope of a line of fit, what can you use?

• Any two points on the line

• Only the data points

• The highest and lowest points

• The points with the largest x-values

What does a slope of 0.375 mean in the context of the lesson?

• There are 0.375 tons of food for every volunteer

• There are 3.75 tons of food for every volunteer

• There are 3.75 volunteers for every ton of food

• There are 0.375 volunteers for every ton of food

In Example 1, what is the y-intercept of the line of fit for Mia's piano practice?

• 6

• 1

• 11

• 2.5

What does the y-intercept represent in the context of Mia's piano practice?

• The average number of mistakes per hour

• The number of mistakes she makes after practicing for one hour

• The number of mistakes she makes without any practice

• The total time she spends practicing

What is the equation of the line of fit for the scatter plot showing the number of text messages sent and received by different age groups?

• y = -80x - 4500

• y = 80x - 4500

• y = -80x + 4500

• y = 80x + 4500

What is a limitation of using the line of fit to predict text messages for ages beyond the given data?

• The predictions are only valid for ages 0-10

• The predictions do not change

• The predictions are always accurate

• The predictions may result in negative values

In Example 2, what is the slope of the line of fit for the company's advertising and sales data?

• 250

• 5.56

• 225

• 50

What does the slope of 5.56 represent in the context of the company's advertising and sales data?

• The total sales made

• The increase in sales for every extra thousand dollars spent on advertising

• The total amount spent on advertising

• The increase in sales for every extra dollar spent on advertising

If the company spends $60,000 on advertising, what is the predicted sales amount?

• $600,000

• $558,600

• $500,000

• $225,000