8.SP.3: Interpret a Linear Model
Also written as 8.SP.A.3 and CCSS.MATH.CONTENT.8.SP.A.3 · Cluster: Investigate patterns of association in bivariate data.
The Official Wording
Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
Common Core State Standards, Grade 8, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 8.SP.3 Means in Plain English
Eighth graders read a fitted line in context. If s = 6h + 58 models test scores from hours studied, the slope says each extra hour goes with about 6 more points, and the intercept is the predicted score with no study. Then they use the equation to predict.
Part of the skill is knowing the limits: an intercept can be meaningless, and predictions far outside the data, like a car priced below zero, are not trustworthy. High school interprets slope and intercept the same way for least-squares lines (HSS-ID.7).
8.SP.3 I Can Statements
- I can explain a fitted line’s slope in the units of the data.
- I can explain what the intercept means, or why it does not.
- I can use a linear model to predict and spot unreasonable predictions.
8.SP.3 Worked Example
A fitted line for used-car prices, read number by number, then pushed until it breaks.
A line fitted to the ages and prices of 12 used cars of one model, aged 1 to 10 years, is p = 24 - 2.1a, with a in years and p in thousands of dollars. What do 24 and -2.1 mean? Predict the price of a 6-year-old car, then try a 15-year-old one.
- Name what each letter stands for, with its unit.a = age in years; p = price in thousands of dollars
- The slope is the change in p for each 1 more of a, said in context.-2.1: each extra year of age goes with about $2,100 less in price
- The intercept is the value of p when a = 0.24: a brand-new car of this model is predicted at about $24,000
- Substitute 6 for a to predict.p = 24 - 2.1 × 6 = 24 - 12.6 = 11.4, about $11,400
- Try an age far outside the data, which ran from 1 to 10 years.p = 24 - 2.1 × 15 = -7.5, a negative price: the model breaks
Check it: Rebuild the prediction in dollars: 6 years at $2,100 each is $12,600 off $24,000, which leaves $11,400. And 6 years sits inside the 1 to 10 year range of the data, so the prediction is a fair use of the model.
Common Mistakes with 8.SP.3
Giving the slope without units or context
“The slope is -2.1.”
Try this: Finish the sentence “for each extra year of age, the price changes by…” with the number and both units.
Trusting predictions far outside the data
“A 15-year-old car costs -$7,500.”
Try this: Compare the input with the data’s range first; the cars were 1 to 10 years old, so 15 is outside the model.
Swapping slope and intercept
“A new car costs $2,100 and loses $24,000 a year.”
Try this: Match each number to its role: the number multiplying a is the rate per year, the number standing alone is the start.
Where 8.SP.3 Fits
Practice 8.SP.3
Quick Check
- A model for a plant’s height is h = 0.8d + 5, in centimeters after d days. What does 0.8 mean?
- In the same model, what does 5 mean?
- A runner’s mile time is modeled by m = 12 - 0.5w, in minutes after w weeks of training. Predict the time after 6 weeks.