IM Alg1.3.4 Lesson: Linear Models
What do you notice? What do you wonder?
Use the applet below to help answer the questions.
Estimate a value for the slope of the line. What does the value of the slope represent?
Estimate the weight of a box containing 11 oranges. Will this estimate be close to the actual value? Explain your reasoning.
Estimate the weight of a box containing 50 oranges. Will this estimate be close to the actual value? Explain your reasoning.
Estimate the coordinates for the vertical intercept of the line you drew. What does the -coordinate for this point represent?
Which point(s) are best fit by your linear model? How did you decide?
Which point(s) are fit the least well by your linear model? How did you decide?
The scatter plot shows the sale price of several food items, y, and the cost of the ingredients used to produce those items, x, as well as a line that models the data.
The line is also represented by the equation . What is the predicted sale price of an item that has ingredients that cost $1.50? Explain or show your reasoning.
What is the predicted ingredient cost of an item that has a sale price of $7? Explain or show your reasoning.
What is the slope of the linear model? What does that mean in this situation?
What is the -intercept of the linear model? What does this mean in this situation? Does this make sense?
Here is a scatter plot.
Using the horizontal axis for and the vertical axis for , interpret the slope of the linear model in the situation shown in the scatter plot.
If the linear relationship continues to hold for the situation, interpret the -intercept of the linear model in the situation provided.
Here is another scatter plot.
Using the horizontal axis for and the vertical axis for , interpret the slope of the linear model in the situation shown in the scatter plot.
If the linear relationship continues to hold for the situation, interpret the -intercept of the linear model in the situation provided.
Here is another scatter plot.
Using the horizontal axis for and the vertical axis for , interpret the slope of the linear model in the situation shown in the scatter plot.
If the linear relationship continues to hold for the situation, interpret the -intercept of the linear model in the situation provided.
Here is another scatter plot.
Using the horizontal axis for and the vertical axis for , interpret the slope of the linear model in the situation shown in the scatter plot.
Clare, Diego, and Elena collect data on the mass and fuel economy of cars at different dealerships.
Clare finds the line of best fit for data she collected for 12 used cars at a used car dealership. The line of best fit is where is the car’s mass, in kilograms, and is the fuel economy, in miles per gallon.
Interpret the slope and -intercept of Clare’s line of best fit in this situation.Diego made a scatter plot for the data he collected for 10 new cars at a different dealership. Elena made a table for data she collected on 11 hybrid cars at another dealership. 
If the linear relationship continues to hold for the situation, interpret the -intercept of the linear model in the situation provided.
Diego looks at the data for new cars and used cars. He claims that the fuel economy of new cars decreases as the mass increases. He also claims that the fuel economy of used cars increases as the mass increases. Do you agree with Diego’s claims? Explain your reasoning.
Elena looks at the data for hybrid cars and correctly claims that the fuel economy decreases as the mass increases. How could Elena compare the decrease in fuel economy as mass increases for hybrid cars to the decrease in fuel economy as mass increases for new cars? Explain your reasoning.