The Line of Best Fit

A straight line through a cloud of points.

10 problems · about 19 minutes · 8.SP.A.2, 8.SP.A.3

What this lesson teaches

The child draws a line of best fit and interprets its slope and intercept in context.

A line of best fit runs through the middle of the points, not through any particular one.
Its slope describes how one quantity changes with the other.
Predictions are only trustworthy across the range of the data.

From earlier lessons. Loosen up before the new work.

3 problems

Review — Scatter Plots and Association: Fitted line y = 2x + 3. Predict for x = 6.
Answer 15
Why 15.
Review — Volume of Cones, Cylinders, and Spheres: A cylinder holds 210. Its matching cone holds?
Answer 70
Why 70.
Review — Distance Between Two Points: From (0, 0) to (8, 15). Distance?
Answer 17
Why 17.

Straightforward practice. Get the method working first.

3 problems

y = 5x + 2. What is y at x = 3?
Answer 17
Why 17.
y = 2x + 1. What is y at x = 6?
Answer 13
Why 12 + 1.
Must a line of best fit pass through a data point? 1 for yes, 0 for no.
Answer 0
Why It summarises the trend.

The same ideas with more to keep track of.

2 problems

A slope of 4 on a cost-against-items plot. Cost per item?
Answer 4
Why Rise per one across.
Is predicting far outside the data reliable? 1 for yes, 0 for no.
Answer 0
Why The trend may not hold.

Mixed problems. Work out what kind of question it is before you start.

2 problems

The Prediction: A line of best fit is y = 3x + 5. What is y when x is 4?
Answer 17
Why 17.
The Starting Value: Same line. What is y when x is 0?
Answer 5
Why 5.