1. Constant Rate of Change and Direct Variation Lesson 7-4 in the Pre-Algebra textbook

2. Linear Relationships Graphs that have straight lines
Constant rate of change (the rate of change between any two points is the same)
Example:
TIME (hrs)
DISTANCE (mi)

4. Using a graph to find a constant rate of change:
𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒= 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥

5. Some linear relationships are also proportional
Some linear relationships are also proportional. That is, the ratio of each non-zero y-value compared to the corresponding x-value is the same. Example:

6. Using graphs to identify proportional relationships: The number of gallons of water in a pool as it is being filled is recorded in the table below. Determine if there is a proportional relationship between the number of gallons and the time.
Gallons x
Hours y

7. Direct Variation:
A special type of linear equation that describes constant rate of change.
The graph of a direct variation always passes through the origin and represents a proportional linear relationship.

8. In the equation y = kx, k is called the constant of variation or constant of proportionality.
The direct variation y = kx can be written as 𝑘= 𝑦 𝑥 (You can see that x and y vary in such a way that they have a constant ratio, k.)

9. Use direct variation to solve problems:
Step 1: Solve for k.
Step 2: Use k to write an equation.
*Predict how much 25 pounds of coffee will cost.
Number of Pounds of Coffee
Total Sales ($)
Rate of Change (lbs/$) x y
𝑘= 𝑥 𝑦 1 2 4 3 6 8

10. Use direct variation to solve problems:
*Write an equation that relates the distance a sloth travels to the time.
*Predict how long it will take a sloth to travel 30 feet.

11. Classwork: p #1-6