Pre-Algebra
Data and graphs
Line of best fit and linear association
20 practice questions
0 video lessons
Theory + worked examples
Line of Best Fit and Linear Association
Texas Pre-Algebra (TEKS) • Standard 8.5(C) • Data & Graphs
Line of Best Fit and Linear Association is a topic in Data & Graphs in the Texas Essential Knowledge and Skills. It is aligned to Standard 8.5(C), which requires students to fit a line to scatter-plot data and describe linear association.
The line of best fit models the linear trend in a scatter plot and lets you make predictions.
Theory
The line of best fit is a straight line that models the trend in a scatter plot.
A tight cluster around the line means a strong linear association; use the line to predict.
A line modeling the trend.
Line of best fit.
A linear model:
\[y=mx+b\]
Substitute an \(x\) to predict \(y\).
How to use a line of best fit
- Draw the line through the trend.
- Find its equation \(y=mx+b\).
- Substitute to predict.
- Judge the fit by the clustering.
Example 1 — Predict
A best-fit line is \(y=0.9x+1\). Predict \(y\) at \(x=6\).
Solution
Substitute.
| \(0.9(6)+1\) | \(=\) | \(6.4\) |
Example 2 — Slope
In \(y=0.9x+1\), what does \(0.9\) mean?
Solution
The rate of change per unit \(x\).
Example 3 — Strong fit
When is a linear association strong?
Solution
When points cluster tightly around the line.
Example 4 — Direction
A positive slope means what association?
Solution
Positive linear association.
Common pitfalls
A trend line is a model, not exact.
Prediction far outside the data is risky.
Association is not causation.
Frequently asked questions
What is the line of best fit?
A line modeling the linear trend.
What is it used for?
Making predictions.
What is strong association?
Points clustering tightly around the line.
What does a positive slope mean?
Positive association.
More in Data and graphs