Grade 8 Scatter Plots: Line of Best Fit

Worked examples

Real problems from the practice worksheets, solved one step at a time.

1. Example 1

   x = Age of car (years) · y = Value ($ thousands)

   Data: Age of car (years) (x) and Value ($ thousands) (y)

   x	2	3	4	5
   y	23	21	18	16
   x	6	7	8	9
   y	13	9	6	2

   The line of best fit passes through (3, 21) and (8, 6). What is the y-intercept of the line?

   1. Slope = change in y ÷ change in x (rise over run), using the two points on the line.
   2. Change in y: 6 − 21 = −15. Change in x: 8 − 3 = 5.
   3. Slope = −15 ÷ 5 = −3.
   4. Use b = y − m·x with the point (3, 21): b = 21 − (−3) × 3 = 21 − (−9) = 30.
   5. So the y-intercept is 30 (the line crosses the y-axis at (0, 30)).

   Answer: 30

2. Example 2

   x = Price ($) · y = Shirts sold

   Data: Price ($) (x) and Shirts sold (y)

   x	10	12	14	16
   y	82	78	70	66
   x	18	20	22	24
   y	62	58	58	54

   The line of best fit passes through (12, 76) and (22, 56). What is the slope of the line?

   1. Slope = change in y ÷ change in x (rise over run), using the two points on the line.
   2. Change in y: 56 − 76 = −20. Change in x: 22 − 12 = 10.
   3. Slope = −20 ÷ 10 = −2.
   4. So the slope is −2.

   Answer: −2

3. Example 3

   x = Temperature (°F) · y = Cones sold

   Data: Temperature (°F) (x) and Cones sold (y)

   x	64	68	72	76
   y	125	135	157	167
   x	80	84	88	92
   y	183	205	215	237

   The line of best fit is y = 4x − 134. Is the point (80, 183) above or below the line?

   1. Find the line's y-value at x = 80: y = 4 × 80 − 134 = 320 − 134 = 186.
   2. The point's y-value is 183, which is less than 186.
   3. So the point (80, 183) is below the line.

   Answer: below