Georgia 8.FGR.6.3
The Standard
Explain the meaning of the predicted slope (rate of change) and the predicted intercept (constant term) of a linear model in the context of the data.
Georgia's K-12 Mathematics Standards · Solve practical, linear problems involving situations using bivariate quantitative data.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students explain how much the predicted response changes for each one-unit increase in the input. They explain what the intercept predicts when the input is zero, using context and correct units.
What Mastery Looks Like
- Given a model and context, students identify both values and write complete interpretations with units. They use the word predicted and decide whether the intercept is reasonable in the situation.
Common Misconceptions
- Students may swap the meanings of slope and intercept. They often leave out units or describe predictions as exact values. They may assume the intercept is meaningful even when zero is outside the data range.
How to Assess It
- Exit ticket: A delivery cost model is ŷ = 1.80x + 6, where x is miles and ŷ is dollars. Explain 1.80 and 6 in context, with units.
Lesson moves
Ways to Teach It
Stack paper cups, measure total height for several stack sizes, fit a line, and explain the slope and intercept with units.
Ask: In a taxi fare model using miles and dollars, why does a $4 intercept make sense, and what does a 2.50 slope mean?
Run a card sort matching four equations to context cards and separate cards that correctly interpret each slope and intercept.
Use a school fundraiser model relating items sold to predicted profit, then discuss what the slope and intercept mean for planning.
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Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts.
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