2.5 Model Direct Variation

1. 2.5 Model Direct Variation Objectives: Construct a model for direct variation Use the model to show the relationship between x and y. Common Core Standards: A-CED-2, F-LE-2 Assessments: Define all vocab for this section Do worksheet 2-5

2. Direct Variation • Y=ax • The constant “a”(which cant be zero) is called the constant of variation • Explains how y differs from x

3. Write and graph a direct variation equation EXAMPLE 1 Write and graph a direct variation equation that has (– 4, 8) as a solution. Start with y=ax Substitute in y and x values, and solve for a. Re-write equation

4. Hailstones form when strong updrafts support ice particles high in clouds, where water droplets freeze onto the particles. The diagram shows a hailstone at two different times during its formation. EXAMPLE 2 a. Write an equation that gives the hailstone’s diameter d(in inches) after tminutes if you assume the diameter varies directly with the time the hailstone takes to form. b. Using your equation from part (a), predict the diameter of the hailstone after 20 minutes.

5. Use ratios to identify direct variation EXAMPLE 3 Sharks Great white sharks have triangular teeth. The table below gives the length of a side of a tooth and the body length for each of six great white sharks. Tell whether tooth length and body length show direct variation. If so, write an equation that relates the quantities.

6. 350 215 290 430 565 695 121 = 119 121 120 119 120 2.9 5.8 3.6 2.4 1.8 4.7 b t ANSWER Because the ratios are approximately equal, the data show direct variation. An equation relating tooth length and body length is = 120, or b = 120t. Use ratios to identify direct variation EXAMPLE 3