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▪ Scatter Plot A: The reaction time estimated by the linear model for a newborn is 400 milliseconds.
▪ Scatter Plot B: The price estimated by the linear model for purchasing zero bananas is $0.04.
▪ Scatter Plot C: The xed cost to install ooring is $87.
▪ Scatter Plot D: 25 cubic centimeters is the volume estimated by the linear model for
a temperature of zero degrees Celsius.
Activity Synthesis
The purpose of this discussion is for students to describe the rate of change and the vertical intercept using the context in each graph.
Ask students:
• “Why is the intercept for the medical items not ?” (Companies will still try to charge money for items that cost nothing to produce. They need to pay for the salaries of their workers, research and development, as well as other things that require the company to make money more than just the cost of making the item. It may also be the case that it does not make sense to interpret the -intercept since we have no evidence to believe that the same linear relationship will hold there.)
• “Why is the intercept for the bananas not ?” (A linear model is not exact even for the data it is based on. It is an approximation based on the data in the scatter plot. It is possible that it represents the weight of the bag that bananas were placed in. It is also possible that this value does not make sense since there is no evidence to believe the same linear relationship will hold near zero.)
• “How do you interpret the slope for each equation?” (You know the slope is the change in divided by the change in so you look at the labels on the scatter plot and talk about for each increase of one on the label, on average, there is a decrease (if the slope is negative) or increase (if the slope is positive) in the variable represented by the direction.)
• “When might it make sense to interpret the -intercept for a linear model?” (When values around 0 are in the range of the data used to create the model. In other cases, care should be taken to put too much faith in the answer.)
Lesson Synthesis
The goal of this discussion is for students to make connections between bivariate data, a linear model, and the context of the data.
• “How do you represent bivariate numerical data? How do you represent bivariate categorical data?” (You could use a two-way table for categorical data and a scatter plot for numerical data.)
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Teacher Guide Algebra