Grade 8 Scatter Plots: Making Predictions

Worked examples

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

1. Example 1

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

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

   x	60	63	66	69
   y	42	48	62	74
   x	72	75	78	81
   y	83	89	93	105

   The line of best fit is y = 3x − 137, where x is the temperature and y is the number of cones sold. Predict the number of cones sold when the temperature is 57.

   1. The line is y = 3x − 137, where x is the temperature. Put in x = 57.
   2. y = 3 × 57 − 137 = 171 − 137 = 34.
   3. So the line predicts the number of cones sold is 34.

   Answer: 34

2. Example 2

   x = Minutes of exercise · y = Calories burned

   Data: Minutes of exercise (x) and Calories burned (y)

   x	10	15	20	25
   y	87	121	167	201
   x	30	35	40	45
   y	241	287	321	367

   The line of best fit is y = 8x + 4, where x is the minutes of exercise and y is the calories burned. Predict the calories burned when the minutes of exercise is 50.

   1. The line is y = 8x + 4, where x is the minutes of exercise. Put in x = 50.
   2. y = 8 × 50 + 4 = 400 + 4 = 404.
   3. So the line predicts the calories burned is 404.

   Answer: 404

3. Example 3

   x = Minutes of exercise · y = Calories burned

   Data: Minutes of exercise (x) and Calories burned (y)

   x	10	15	20	25
   y	113	136	196	233
   x	30	35	40	45
   y	278	331	361	428

   The line of best fit passes through (15, 147) and (40, 372). Predict the calories burned when the minutes of exercise is 44.

   1. Slope = change in y ÷ change in x (rise over run), using the two points on the line.
   2. Change in y: 372 − 147 = 225. Change in x: 40 − 15 = 25.
   3. Slope = 225 ÷ 25 = 9.
   4. Use b = y − m·x with the point (15, 147): b = 147 − 9 × 15 = 147 − 135 = 12.
   5. The line is y = 9x + 12. Put in x = 44: y = 9 × 44 + 12 = 396 + 12 = 408.
   6. So the line predicts the calories burned is 408.

   Answer: 408