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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). In Statistics and Data Analysis, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.

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.
  3. Connect the result back to Line of Best Fit so the method and meaning are both clear.
  4. Check the result against the original representation before writing the final answer.

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.
  5. Identify the Algebra I structure before choosing a calculation.

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.
  5. Identify the Algebra I structure before choosing a calculation.

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.
  5. Identify the Algebra I structure before choosing a calculation.

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.
  5. Identify the Algebra I structure before choosing a calculation.

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.
  5. Identify the Algebra I structure before choosing a calculation.

Answer: Value when x = 0

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