Grade 8 · Statistics & Modeling · MAT-08-SP-004
Use Linear Models to Make Predictions
Represent and solve use linear models to make predictions problems using precise mathematical notation, multiple representations, and justified reasoning.
Learning objectives
What you should be able to do
- Represent and solve use linear models to make predictions problems using precise mathematical notation, multiple representations, and justified reasoning.
- Interpret and verify use linear models to make predictions results in context, including units, constraints, and reasonableness.
Prerequisite check
Make sure the foundation is ready.
Grade 8 uses this prerequisite as active knowledge in a more formal representation.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Use Linear Models to Make Predictions belongs to statistics & modeling. Identify the governing property or relationship before choosing a procedure.
Multiple representations
Represent use linear models to make predictions numerically and symbolically, then connect it to the Grade 8 Math Box. Tables, graphs, equations, coordinate models, diagrams, and verbal descriptions must agree.
Verification and interpretation
Check with substitution, an inverse operation, an equivalent representation, geometric invariants, estimation, or context. State whether the result is exact or approximate and preserve relevant units and constraints.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Scatter Plot Lab
- Model use linear models to make predictions in the Math Box.
- Change one input and predict which quantities or invariants should change.
- Explain what the visual, equation, and numerical result say about the same relationship.
Worked examples
Twenty different ways to see the concept work.
Use y=2x+5 to predict y for x=5.
15Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+6 to predict y for x=6.
-6Substitute into the fitted model and interpret the result as a prediction.
Use y=2x+7 to predict y for x=7.
21Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+8 to predict y for x=8.
-8Substitute into the fitted model and interpret the result as a prediction.
Use y=2x+9 to predict y for x=9.
27Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+10 to predict y for x=10.
-10Substitute into the fitted model and interpret the result as a prediction.
Use y=2x+11 to predict y for x=11.
33Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+12 to predict y for x=12.
-12Substitute into the fitted model and interpret the result as a prediction.
Use y=2x+5 to predict y for x=13.
31Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+6 to predict y for x=14.
-22Substitute into the fitted model and interpret the result as a prediction.
Use y=2x+7 to predict y for x=5.
17Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+8 to predict y for x=6.
-4Substitute into the fitted model and interpret the result as a prediction.
Use y=2x+9 to predict y for x=7.
23Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+10 to predict y for x=8.
-6Substitute into the fitted model and interpret the result as a prediction.
Use y=2x+11 to predict y for x=9.
29Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+12 to predict y for x=10.
-8Substitute into the fitted model and interpret the result as a prediction.
Use y=2x+5 to predict y for x=11.
27Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+6 to predict y for x=12.
-18Substitute into the fitted model and interpret the result as a prediction.
Use y=2x+7 to predict y for x=13.
33Substitute into the fitted model and interpret the result as a prediction.
Use y=-2x+8 to predict y for x=14.
-20Substitute into the fitted model and interpret the result as a prediction.
Practice
Guided practice with hints
01Use y=2x+9 to predict y for x=5.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: 19
02Use y=-2x+10 to predict y for x=6.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: -2
03Use y=2x+11 to predict y for x=7.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: 25
04Use y=-2x+12 to predict y for x=8.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: -4
05Use y=2x+5 to predict y for x=9.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: 23
06Use y=-2x+6 to predict y for x=10.
Hint: Represent the structure first, calculate carefully, then verify with a second representation or substitution.
Answer: -14
Practice
Independent practice
01Use y=2x+7 to predict y for x=11.
Answer: 29
02Use y=-2x+8 to predict y for x=12.
Answer: -16
03Use y=2x+9 to predict y for x=13.
Answer: 35
04Use y=-2x+10 to predict y for x=14.
Answer: -18
05Use y=2x+11 to predict y for x=5.
Answer: 21
06Use y=-2x+12 to predict y for x=6.
Answer: 0
07Use y=2x+5 to predict y for x=7.
Answer: 19
08Use y=-2x+6 to predict y for x=8.
Answer: -10
Common mistakes
Learn to catch the error, not just the answer.
Association alone does not establish cause.
A fitted line summarizes a trend and produces estimates.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Analyze paired numerical data for trends and make cautious model-based predictions.
- Compare categorical groups with conditional percentages in two-way tables.
Challenge problems
Use y=2x+7 to predict y for x=9.
25
Use y=-2x+8 to predict y for x=10.
-12
Use y=2x+9 to predict y for x=11.
31
Use y=-2x+10 to predict y for x=12.
-14
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 8 Algebra & Modeling Sprint
Solve use linear models to make predictions problems and justify each result with a valid verification method.
Practice
Mastery check
01Use y=2x+11 to predict y for x=13.
Answer: 37
02Use y=-2x+12 to predict y for x=14.
Answer: -16
03Use y=2x+5 to predict y for x=5.
Answer: 15
04Use y=-2x+6 to predict y for x=6.
Answer: -6
05Use y=2x+7 to predict y for x=7.
Answer: 21
06Use y=-2x+8 to predict y for x=8.
Answer: -8
07Use y=2x+9 to predict y for x=9.
Answer: 27
08Use y=-2x+10 to predict y for x=10.
Answer: -10
Terminology
Words to know
- bivariate data
- Paired measurements of two variables for the same observations.
- association
- A pattern showing how variables or categories vary together.
- line of best fit
- A line summarizing an approximately linear scatter-plot trend.
- conditional relative frequency
- A category frequency divided by the relevant row or column total.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade 8 instructional guidance, mathematical practices, modeling, and progression toward high-school mathematics.Common Core State Standards for Mathematics — Grade 8
Grade-level expectations for real numbers, equations, functions, geometry, and statistics.Principles to Actions: Ensuring Mathematical Success for All
Research-informed emphasis on reasoning, representations, discourse, productive struggle, and conceptual understanding.