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

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)

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

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:

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

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.

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.)

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

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.

Classwork: p.379-80 #1-6 1. 2. 3. 4. 5. 6.