CCSS.Math.Content.HSS-ID.C.7
The standard
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Common Core State Standards for Mathematics
What this standard means
Students need to explain what the slope and intercept mean for a line fitted to data. They should connect the slope to a rate, using units, and describe the intercept as the predicted value when the input is zero.
Mastery means students can say, for example, “for each extra hour studied, the predicted score rises by 4 points,” not just “the slope is 4.” They also need to judge whether the intercept makes sense in context. Common trouble spots are leaving off units, mixing up x and y, and treating the intercept as always meaningful.
Ways to teach it
- Hands-on activity: Give pairs scatterplots with fitted lines and have them label the slope and intercept using sticky notes with units.
- Writing prompt: Ask students to explain what the slope and intercept mean for a model connecting shoe size and height.
- Quick assessment: Show y = 2.5x + 18 for taxi cost and ask students to interpret both numbers in one sentence each.
- Real-world connection: Use a phone plan with a startup fee and monthly cost to connect intercept to fixed cost and slope to repeated cost.
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Related standards
- CCSS.Math.Content.8.SP.A.3
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
- CCSS.Math.Content.HSF-LE.B.5
Interpret the parameters in a linear or exponential function in terms of a context.
- CCSS.Math.Content.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of...
- CCSS.Math.Content.HSS-ID.C
Interpret linear models