8.SP.2: Fit a Line to a Scatter Plot
Also written as 8.SP.A.2 and CCSS.MATH.CONTENT.8.SP.A.2 · Cluster: Investigate patterns of association in bivariate data.
The Official Wording
Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
Common Core State Standards, Grade 8, Statistics & Probability · Read it at the source · Checked October 14, 2026
What 8.SP.2 Means in Plain English
Eighth graders decide whether a scatter plot looks linear, then lay a line through it by eye, keeping about as many points above as below. For eight students’ heights and arm spans, y = x runs through the band, and every point sits within 2 cm of it.
Judging fit is the new habit: points hugging the line mean a good model, a wide scatter a weak one, and a bend means a line is the wrong tool. 8.SP.3 puts the line’s equation to work; high school measures fit with residuals (HSS-ID.6).
8.SP.2 I Can Statements
- I can tell whether a scatter plot suggests a linear model.
- I can draw a line by eye with points balanced on both sides.
- I can judge a line’s fit by how close the points are.
8.SP.2 Worked Example
Eight students’ heights and arm spans, a line drawn by eye, and a check of how close the points sit to it.
Eight students measured their height and arm span in centimeters: (150, 148), (155, 156), (158, 157), (162, 163), (165, 164), (170, 171), (173, 172), (178, 179). Fit a line by eye and judge how well it fits.
- Plot the points and look at the shape first. They rise in a narrow, straight band, so a line is a sensible model.Positive and linear: fit a line
- Lay a ruler along the band so points fall on both sides, rather than through the first and last points.Line through (150, 150) and (180, 180)
- Find the equation from two points on the line, not two data points.slope = (180 - 150) ÷ (180 - 150) = 1, so y = x
- Measure each point straight up or down to the line, where the predicted arm span equals the height.148 is 2 below the line; the other seven are 1 above or 1 below
- Weigh both sides and the distances: four points above, four below, none more than 2 cm away.A close fit: arm span ≈ height
Check it: List the sides: (155, 156), (162, 163), (170, 171) and (178, 179) are above; (150, 148), (158, 157), (165, 164) and (173, 172) are below. Four and four, so the line is not tilted toward either side.
Common Mistakes with 8.SP.2
Joining the first and last points
A line through (150, 148) and (178, 179) only
Try this: Ignore the end points and follow the middle of the band, checking that roughly half the points fall on each side.
Fitting a line to a curve
A straight line through points that rise steeply and then level off
Try this: Check the shape before drawing: if the points bend, say a line is a poor model rather than forcing one through.
Measuring distance at a slant
Distance to the line measured with a ruler held at right angles to the line
Try this: Measure straight up or down from each point to the line, since the model predicts a y value for each x.
Where 8.SP.2 Fits
Practice 8.SP.2
Quick Check
- Ten points rise in a narrow band, and a fitted line has 9 points above it and 1 below. Is it a good line?
- A fitted line passes through (0, 12) and (10, 32). What is its equation?
- Plot A’s points all sit within 1 unit of its line; plot B’s are up to 8 units away. Which line is the better model?