Slope and Direct Variation.ink
Slope and Direct Variation
Section 5-2
Objectives
Write and graph direct variation equations.
Solve problems involving direct variation.
1
Slope and Direct Variation.ink
What is direct variation?
2
Slope and Direct Variation.ink
Example 1: Slope and Constant of Variation
Name the constant of variation for the equation. Then find the slope of the line that
passes through each pair of points.
3
Slope and Direct Variation.ink
Example 1: Slope and Constant of Variation
Name the constant of variation for the equation. Then find the slope of the line that
passes through each pair of points.
4
Slope and Direct Variation.ink
Graphing Direct Variation Equations
k>0
y = 4x
5
Slope and Direct Variation.ink
Graphing Direct Variation Equations
k<0
y = -1/3 x
6
Slope and Direct Variation.ink
Key Concept: Direct Variation Graphs
Words:
- in the form y = kx
- always passes through the origin
Positive: k > 0
Negative: k < 0
7
Slope and Direct Variation.ink
Example 2: Write and Solve a Direct Variation Equation
Suppose y varies directly as x, and y = 28 when x = 7.
a. Write a direct variation equation.
b. Use the direct variation equation to find when x when y = 52.
8
Slope and Direct Variation.ink
Example 3: Solve Problems Involving Direct Variation
A flock of snow geese migrated 375 miles in 7.5 hours.
a. Write a direct variation equation for the distance flown in any
time.
b. How long would it take the geese to migrate 3000 miles?
9
Slope and Direct Variation.ink
10
Slope and Direct Variation.ink
Lesson Overview
1.
2.
3.
4.
Direct variation
Constant of variation
Slope and Constant of variation
Direct variation
k>0
k<0
5. Using direct variation
*Assessment: 5-2 Worksheet*
11