Constant rate of change

  • The constant rate of change refers to the rate at which one quantity changes in relation to another in a linear relationship. It is the same throughout the entire interval or period being measured.
  • It is often described as the slope of a line on a graph.

  • The formula to calculate the constant rate of change (or slope) is:
  • Where:
  • Δy is the change in the dependent variable (vertical change).
  • Δx is the change in the independent variable (horizontal change).

Learn with an example

👉 What is the rate of change?

Write your answer as a decimal or integer.

_____  seconds per item

✈️ Find any two points on the line.

  • Two points on the line are (0, 20) and (50, 50). Put those points into the slope formula.
  • slope = change in y / change in x
  • = 50 − 20 / 50 − 0 ——-> Plugin (020) and (5050)
  • = 30/50 ——-> Subtract
  • = 3/5 ——> Simplify
  • = 0.6 ——-> Write as a decimal
  • The slope is 0.6. The rate of change is 0.60 seconds per item.

👉 What is the rate of change?

Write your answer as a decimal or integer.

_____  flowers per seed packet

✈️ Find any two points on the line.

  • Two points on the line are (0, 10) and (20, 40). Put those points into the slope formula.
  • slope = change in y / change in x
  • = 40 − 10 / 20 − 0 ——-> Plugin (010) and (2040)
  • = 30/20 —–> Subtract
  • = 3/2 ——> Simplify
  • = 1.5 ——-> Write as a decimal
  • The slope is 1.5. The rate of change is 1.50 flowers per seed packet.

👉 What is the rate of change?

Write your answer as a decimal or integer.

_______  pictures per day

✈️ Find any two points on the line.

  • Two points on the line are (0, 2) and (1, 4). Put those points into the slope formula.
  • slope = change in y / change in x
  • = 4 − 2 / 1 − 0 ——> Plugin (02) and (14)
  •  = 2/1 ——> Subtract
  • = 2 —–> Simplify
  • The slope is 2. The rate of change is 2 pictures per day.

Let’s practice! 🖊️