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Line of Best Fit

A free Algebra I lesson from the “Statistics and Data Analysis” unit, with a worked example and practice problems including step-by-step solutions.

A line of best fit (also called a trend line or linear regression line) is the line that best summarizes a scatter plot. Its slope tells the rate of change between variables; its y-intercept is the predicted value when x = 0. Use it to predict new outcomes. Interpolation is prediction inside the data range; extrapolation is outside (riskier).

What you'll learn

Why it matters: Stock analysts, weather forecasters, and sports coaches all use trend lines to make predictions from past data.

Worked example

Problem. A best-fit line is y = 5x + 20 for (hours studied, test score). Predict the score after 4 hours.

  1. Substitute x = 4: y = 5(4) + 20.
  2. = 20 + 20 = 40.

Answer: 40

Practice problems

1. For y = 2x + 50, predict y when x = 10.

Show solution
  1. Warm-up: First identify exactly what the question is asking: For y = 2x + 50, predict y when x = 10.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. y = 20 + 50 = 70.
  4. Check the result by substituting or estimating: the response should match 70 and make sense in the original problem.

Answer: 70

2. For y = -3x + 100, predict y when x = 5.

Show solution
  1. Warm-up: First identify exactly what the question is asking: For y = -3x + 100, predict y when x = 5.
  2. For signed numbers, track both distance from zero and direction so the sign of the answer makes sense.
  3. y = -15 + 100 = 85.
  4. Check the result by substituting or estimating: the response should match 85 and make sense in the original problem.

Answer: 85

3. For y = 0.5x + 10, predict y when x = 20.

Show solution
  1. Warm-up: First identify exactly what the question is asking: For y = 0.5x + 10, predict y when x = 20.
  2. Use inverse operations to isolate the unknown, and keep both sides balanced at every step.
  3. y = 10 + 10 = 20.
  4. Check the result by substituting or estimating: the response should match 20 and make sense in the original problem.

Answer: 20

4. The slope of a best-fit line tells us:

Choices: Rate of change between variables · Range only

Show solution
  1. Core Practice: First identify exactly what the question is asking: The slope of a best-fit line tells us:
  2. For slope or rate of change, compare vertical change to horizontal change and keep the sign attached to the direction of the change.
  3. Slope = change in y per unit change in x.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Rate of change between variables

5. The y-intercept of a best-fit line is:

Choices: Value when x = 0 · Maximum value

Show solution
  1. Core Practice: First identify exactly what the question is asking: The y-intercept of a best-fit line is:
  2. For intercepts, remember that an x-intercept has y = 0 and a y-intercept has x = 0.
  3. That is the definition of y-intercept.
  4. Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.

Answer: Value when x = 0

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