1. 5.2: Direct Variation

2. Joe shovels snow for his neighbor in Buffalo, NY. Joe’s neighbor typically pays Joe a rate of $5.00 for every inch of snow that falls with each snowstorm. An equation relating Joe’s pay, P, and the amount of snow that falls, h can be modeled by. We can say that Joe’s pay is PROPORTIONAL to the height of the snowfall. In other words, Joe’s pay VARIES DIRECTLY as the height of the snowfall.

3. All direct variation relationships can be represented by the equation where k≠0 k is the coefficient of x and is called the COEFFICIENT of variation. Key Concept: If y varies DIRECTLY as x, When x INCREASES, y increases by the same RATE. When x DECREASES, y decreases by the same RATE.

4. Solving for k, the constant can be written as the ratio: Are the following direct variation relationships? a) The cafeteria charges $1.50 per slice of pizza YES; Cost increases as the number of slices increase b) The temperature and the time of day. NO; Other factors: Storms, cold fronts, etc

5. Identifying a Direct Variation: To determine whether an equation represents direct variation, SOLVE it for y. If you can write the equation in the form, it represents direct variation. Does the equation represent a direct variation? 1) 2.)

6. Writing a Direct Variation Equation: In order to write a direct variation equation, you must first use an ORDERED pair other than (0, 0) to find k. Ex: Suppose y varies directly as x. When x is 12 and y is -4. Find the constant of variation. Write a direct variation equation to represent the problem. What is the values of y when x is 8?

7. Your turn: y varies directly as x. When y = 40 and x = 8. Find the value of y when x = 12.

8. Graphing a Direct Variation Equation: Using your graphing calculator: Graph the following direct variation equations: What is the same about all the graphs? What is different? What is the slope of each line? They all pass through the origin; y-intercept Their “steepness”; slope

9. Writing a Direct Variation From a Table: For the data in each table, tell whether y varies directly with x. If it does, write an equation for the direct variation. 1.) Is k constant? Eq:

10. 2.) Is k constant? Eq:

11. Homework: 5.2 p. 325-327 #’s 14-30 even, 33-37