Grade 8 Functions: Slope

Worked examples

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

1. Example 1

   A line with a slope of 5 passes through (2, −1) and (4, y). What is y?

   1. Slope = change in y ÷ change in x, so change in y = slope × change in x.
   2. Change in x: 4 − 2 = 2.
   3. Change in y: 5 × 2 = 10.
   4. y = −1 + 10 = 9.
   5. So y = 9.

   Answer: 9

2. Example 2

   A car travels at a constant speed. The graph of distance (miles) against time (hours) is a line through (0, 0) and (3, 120). What is the slope of the line, in miles per hour?

   1. Slope = change in y ÷ change in x (rise over run).
   2. From (0, 0) to (3, 120): change in y = 120, change in x = 3.
   3. Slope = 120 ÷ 3 = 40.
   4. So the slope is 40 miles per hour — the car's speed (its unit rate).

   Answer: 40

3. Example 3

   This table shows a linear function: when x = 1, 5, 9, 13, y = −10, 2, 14, 26. What is the rate of change (slope)?

   1. Slope = change in y ÷ change in x (rise over run).
   2. When x goes up by 4 (1 to 5), y changes by 2 − (−10) = 12, so the rate of change is 12 ÷ 4 = 3.
   3. Every pair of neighboring rows changes at the same rate, so the function is linear.
   4. So the rate of change (slope) is 3.

   Answer: 3