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8th grade · Math · Unit 19 of 19

Lines of Best Fit

Predict with a linear model

What your child practices

Using the equation of a line of best fit to make predictions from data, and explaining what the slope and the y-intercept mean in the situation.

New York State Learning Standards learning standard: NY-8.SP.3 · using the equation of a linear model of two-variable data to solve problems, and interpreting its slope and intercept

How we explain it

Children can open this short lesson before they practice.

  1. A line of best fit y = mx + b models two-variable data.
  2. Put a value in for x to predict y.
  3. The slope m is the change in y for each 1 more in x. The intercept b is the predicted y when x is 0.

Example: Test score y and hours of study x fit y = 5x + 60. Predict the score for 4 hours. y = 5 × 4 + 60. y = 20 + 60 = 80. Answer: 80 points

Lines of Best Fit in New York

In the New York State Learning Standards, this is unit 19 of 19 in 8th grade Math, after Distance on a Grid.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A line of best fit for hours of study (x) and test score (y) is y = 6x + 56. What does it predict for x = 6?

    • 68
    • 92
    • 342
    • 36

  2. Question 2

    The model y = 2x + 2 links days since planting (x) and plant height in cm (y). What does the intercept 2 mean?

    • the predicted height on the day it was planted
    • the plant height in cm goes up by 2 each time
    • the number of data points
    • the greatest plant height in cm in the data

  3. Question 3

    Why should you be careful using a linear model far outside the data?

    • the pattern may not continue there
    • the equation stops working at 10
    • slopes change sign outside the data
    • you cannot put big numbers in an equation

  4. Question 4

    The model y = 4x + 18 links weeks of training (x) and push-ups done (y). What does the slope 4 mean?

    • the push-ups done starts at 4
    • the push-ups done is always 4
    • each extra week goes with about 4 more push-ups
    • each extra 4 weeks goes with 1 more push-up

  5. Question 5

    A line of best fit for weeks of training (x) and push-ups done (y) is y = 4x + 13. What does it predict for x = 11?

    • 57
    • 28
    • 147
    • 44

  6. Question 6

    The model y = 4x + 20 links weeks of training (x) and push-ups done (y). For what x does it predict y = 64?

    • 16
    • 12
    • 44
    • 11

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