8th Grade · 8.SP.A.2

The line of best fit in 8th grade

In 8th grade math, a line of best fit is a straight line your child draws by eye through a scatter plot. The line shows the overall pattern of the dots. A scatter plot is a graph with one dot for each person or thing measured in two ways. Your child learns where to place the line and how to tell whether a straight line suits the data at all.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

8.SP.A.2 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.

What it means, in plain words

Lines of best fit are for scatter plots whose dots roughly follow a straight path, called a linear association. The line is a model, a simple picture of the relationship that ignores the small ups and downs. Another name for it is a trend line. In later statistics classes a calculator finds the line with a formula. In 8th grade your child places it by eye.

A good line follows the direction of the dots and runs through the middle of them. About as many dots sit above the line as below it. It does not have to pass through any dot. It does not have to start at $(0, 0)$ either.

Your child also judges how well the line fits. When the dots sit close to the line, the line is a good model. When they are spread far from it, the line is a weak model. When the dots bend into a curve, no straight line fits well, and a straight line is the wrong model for that data.

Your child should be able to:

Decide whether a scatter plot shows a straight path, a curve or no pattern
Draw a line of best fit that follows the dots, with about as many above it as below
Compare two lines and explain which one fits the data better
Judge how good a line is by how close the dots sit to it

Example

Two students draw a line through the same 8 dots. Line A passes through 2 dots, and the other 6 dots are all above it. Line B passes through no dots, with 4 dots just above it and 4 just below. Which is the better line of best fit?

Line A touches 2 dots, but every other dot is on one side, so the line runs too low.
Line B goes through the middle of the group, and every dot is close to it.
Line B is the better line of best fit, because it stays in the middle of all 8 dots.

Example

A scatter plot shows the dots $(1, 1)$ , $(2, 4)$ , $(3, 9)$ , $(4, 16)$ and $(5, 25)$ . Is a straight line a good model for this data?

From $x = 1$ to $x = 2$ the dots rise 3 units. From $x = 4$ to $x = 5$ they rise 9 units.
The rise keeps growing, so the dots bend upward into a curve.
Any straight line misses the middle dots or the end dots by a lot, so a straight line is not a good model for this data.

Where children usually get stuck

Your child draws the line from the first dot to the last dot.
Joining two dots feels like a rule to follow. If either end dot sits high or low, the whole line tilts the wrong way and misses the middle of the group.
What helps. Ask your child to count the dots above the line and below it. If one side has far more, slide or turn the line until the two sides are about even.
Every line your child draws starts at $(0, 0)$ .
The graphs of proportional relationships from 7th grade all started at $(0, 0)$ , so that corner feels like the start of every line.
What helps. Cover the corner of the graph with a finger and look only at the dots. The line should run through the middle of the dots, wherever it then crosses the axes.
Your child draws a straight line through dots that clearly curve and calls it a good fit.
The task looked like "draw a line", so the child never asked whether a straight line belongs there.
What helps. Before any drawing, ask whether the dots look like a straight path, a curve or a cloud. Only the straight path gets a line of best fit.

Try four practice questions

Real 8th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Look at the scatter plot. Drag the explanation cards into order from strongest to weakest explanation of why the line fits the data.
Books Read and Vocabulary Score
Drag a card to move it, or tap a card, then tap where it should go.
1
This line fits well because most points are near the line and roughly balanced above and below it.
2
This line fits well because it rises from left to right, matching the upward trend in the data.
3
This line fits well because every single data point in the scatter plot falls exactly on the line.
Show the answer and how to solve it
Strongest to weakest: the card mentioning both closeness and balance, then the direction-only card, then the perfection card. A good line of fit stays near most points and runs through the middle of the scatter, but points do not need to be perfectly on the line.
1. 1Look at the scatter plot. All 7 points are within 1 grid unit of the red line. The points at (1, 3), (3, 4), (4, 5), (5, 6), and (7, 8) are very close to the line, and the furthest points—(2, 2) and (6, 6)—are each exactly 1 unit away.
2. 2Now check the balance. The point at (1, 3) is 1 unit above the line. The points at (2, 2) and (6, 6) are 1 unit below the line. The other 4 points lie exactly on the line. Ignoring those on the line, 1 point is above and 2 are below—roughly balanced.
3. 3Rank the cards: The card mentioning both closeness and balance is strongest because it uses two pieces of evidence. The direction card is next—a line can point upward and still miss all the points, so direction alone is weak evidence. The perfection card is weakest because 'every single' point is not on the line; three points are 1 unit away.
Common mistake. A common mistake is placing the perfection card higher because it sounds very certain. However, 'every single data point falls exactly on the line' is a false claim—three points are 1 grid unit away—so this card is actually the weakest.
The idea underneath. A good line of fit is strongest when it does two jobs at once: it stays close to most points and runs through the middle of the data pattern.
2On level
Look at the scatter plot and the two candidate lines. Which statement best explains who chose the better-fitting line, and why?
Daily practice time and free throws made
Mia's line
Liam's line
A
Liam's line, because it stays close to the center of the data cluster across the whole graph.
B
Liam's line, because it has a flatter slope that does not overshoot the points on the right.
C
Mia's line, because it passes through two data points exactly.
D
Mia's line, because its slope matches how quickly the data climbs.
Show the answer and how to solve it
The correct choice is the one saying Liam's line is the better fit because it stays close to the center of the data cluster across the whole graph. Liam's line tracks all eight points closely, while Mia's line passes through two points on the left but falls below the cluster on the right.
1. 1Look at the scatter plot. The points show a steady positive association: as practice time increases, free throws made also increases. The data forms a cluster that rises from the lower left toward the upper right, with a fairly consistent upward slope across the full range.
2. 2Check Mia's line. It passes exactly through the data points at x = 2 (y = 3) and x = 4 (y = 4). After x = 4, however, it climbs too slowly: at x = 7 Mia's line is at y = 5.5 while the data point is at y = 7, and at x = 8 it is at y = 6 while the data point is at y = 7. Mia's line falls increasingly below the cluster on the right half of the graph.
3. 3Check Liam's line. It starts at y = 1 on the left and rises to y = 7 at x = 8, matching that data point exactly. At x = 4 it sits at y = 4, also matching the data point there. It stays close to the middle of the cluster from one end of the graph to the other without drifting noticeably above or below.
4. 4The two choices naming Mia rely on misconceptions. One says Mia's line is better because it passes through two data points exactly — but hitting a few exact points is not the rule for best fit; Mia's line drifts well below the cluster after x = 4. The other says Mia's slope matches how quickly the data climbs — but Mia's slope (0.5) is actually too shallow for this trend, so it underestimates every point on the right half of the graph.
5. 5Of the two choices naming Liam, one says his line is better because it has a flatter slope that does not overshoot on the right. A flatter slope is not the rule for best fit; any line could have a low slope and still be far from the data. The other choice says Liam's line stays close to the center of the data cluster across the whole graph — that is the correct criterion for a line of best fit.
Common mistake. A common mistake is choosing the explanation that says Mia's line is better because it passes through two data points exactly. Hitting two exact points looks convincing, but Mia's line drifts far below the rest of the data after x = 4. The real criterion is closeness to the whole cluster, not hitting a few specific points.
The idea underneath. A line of best fit is judged by overall closeness to the data cluster, not by how many points it hits exactly and not just by the steepness or flatness of its slope. A student can guess the right student for the wrong reason, so pay attention to the explanation, not only to the name.
3On level
Drag the cards from top to bottom. Put the line that fits its scatter plot worst first and the line that fits its scatter plot best last.
Drag a card to move it, or tap a card, then tap where it should go.
1
A
2
B
3
C
4
D
Show the answer and how to solve it
From worst to best, the order is C, D, A, B. C has the wrong slope, D is shifted above the cluster, A fits the main cluster with one outlier, and B stays closest to all the data.
1. 1A better-fitting line stays close to most of the points and runs through the center of the cloud, with points balanced on both sides of the line.
2. 2Plot C is the worst fit. Its line is too shallow — it rises by only about 4 units across the grid while the data rises by about 7 units, so the points fan farther and farther above the line as you move to the right.
3. 3Plot D has about the right slope but is shifted roughly 2 units above the cluster, so almost all points sit below the line. Plot A has a well-centered line with the right slope, but the point at (3, 8) sits about 4 units above it. A line that consistently misses the whole cluster is a worse fit than a well-centered line with a single outlier, so A ranks above D.
4. 4Plot B's line passes through seven of the eight points. The remaining point is only 1 unit above it, so B fits best. From worst to best: C, D, A, B.
Common mistake. A common mistake is ranking Plot A below Plot D because A has an outlier. Plot D's line misses the center of the entire cluster, which is a larger overall error than one distant point in A.
The idea underneath. A good line of fit is judged by the whole pattern: it should stay close to most points and run through the center of the data, not just touch a few points.
4Stretch
Which line tilt would be the best starting line of fit for this scatter plot?
A
B
C
D
Show the answer and how to solve it
The answer is the moderate positive line because the scatter plot shows a clear positive association with a rise that is moderate — not gentle and not steep.
1. 1Look at the scatter plot. The points rise steadily as x increases, moving from about (1, 2) on the left up to about (10, 9) on the right. The overall direction is positive.
2. 2The line of fit must tilt upward from left to right. A falling line or a flat line would not match the direction of the data.
3. 3Now judge the steepness. There are two positive-tilting options: a moderate one and a gentler one. The cluster rises about 7 units over 9 x-steps, which is a moderate climb. The gentler option (slope 0.5) would rise only about 4.5 units over that same span — too shallow for this cluster.
4. 4The best starting tilt is the moderate positive line, which matches the overall steepness of the cluster from (1, 2) to (10, 9).
Common mistake. A common mistake is choosing the gentler positive line because both options point upward. The key is to match the overall steepness of the cluster: the data rises roughly 7 units over 9 steps, which fits the moderate positive tilt, not the shallower one.
The idea underneath. To choose a starting line of fit, first match the direction of the association, then match the general steepness of the cluster.