1. Notes: Lesson 5-2 Objective: Write and graph direct variation equations

2. Vocabulary Direct Variation: a relationship between x and y where: if x increases, y also increases if x decreases, y also decreases Direct variation can be described by an equation of the form: Direct variation can be described by an equation of the form: y = kx k is some number and is called the k is some number and is called the constant of variation

3. EXAMPLE 1: You have a job making $6.50 per hour. Let x = # hours you work Let y = total $ you make Equation: y = 6.50x This is an example of direct variation…. If your work you make If your work more hours, you make more money If you work, you make If you work fewer hours, you make less money In this equation, 6.50 is the constant of variation

4. Graph the equation y = 6.50x Make a table. Pick x’s and use the equation to find y’s. x y 01230123 Don’t pick negative numbers for x…. x represents the number of hours you work! 6.50(0)0 6.50(1)6.50 6.50(2)13.00 6.50(3)19.50 hours $ 0 1 2 3 20 18 16 14 12 10 8 6 4 2 IMPORTANT: the line starts here! Don’t go below (0, 0)!

5. EXAMPLE 2: The perimeter P of a regular octagon is 8 times the length of the side, s. Equation: P = 8s like ylike x

6. Graph the equation P = 8s s P Make a table. Pick s’s and use the equation to find P’s 01230123 Don’t pick negative numbers for s…. s represents the number of sides in the octagon! 08(0) 88(1) 168(2) 248(3) 0 1 2 3 30 27 24 21 18 15 12 9 6 3 sides perimeter

7. For other examples, you will be given an equation such as…. y = 5x y = -2x y = ½ x We can graph these by making a table, but using the slope is quicker and easier

8. Example 2-2a Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move up 3 units and right 1 unit. Draw a dot. Step 4Draw a line containing the points. EXAMPLE 3: Graph y = 3x 3 = 3 1

9. Example 2-2a Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move up 1 unit and right 1 unit. Draw a dot. Step 4Draw a line containing the points. EXAMPLE 4: Graph y = x

10. Example 2-3a Step 1Write the slope as a ratio. Step 2Graph (0, 0). Step 3From the point (0, 0), move down 3 units and right 2 units. Draw a dot. Step 4Draw a line containing the points. EXAMPLE 4:

11. Assignment: Lesson 5-2, page 268 #22, 24, 26, 43-46, 48-51