1. Chapter 4: Systems of Equations and Inequalities Section 4.1: Direct Variation

2. Goals: To determine when a function is a direct variation and to solve problems involving direct variation

3. Section 4.1: Direct Variation Direct Variation: a linear function that can be defined by an equation that can be written in the form y = kx, where k ≠ 0 In this case, y varies directly as x k is the constant of variation

4. Section 4.1: Direct Variation Example of direct variation Let's say you want to save some money for an upcoming holiday or event. You have no money saved for this event at the start We can set up an equation: amount saved = dollars * weeks WeekAmount 00 150 2100 3150 4200 5250

5. Section 4.1: Direct Variation Examples Determine whether y varies directly as x. If so, find the constant of variation and write the equation 1.x y 2. x y -2 10 9 3 -4 20 18 6 -6 30 27 9

6. Section 4.1: Direct Variation Examples For each function, determine whether y varies directly as x. If so, find the constant of variation. 3. y = 0.03x 4. 2y = 10x 5. y + 3 = 5x

7. Section 4.1: Direct Variation Examples y varies directly as x 6.y = 20 whe x = 4; find the constant of variation and find y when x = 6 7.y = 14 when x = - 10; find x when y = 7

8. Section 4.1: Direct Variation If y varies directly as x, then for any two ordered pairs (x 1, y 1 ) and (x 2, y 2 ), they form a proportion: y is said to be directly proportional to x The constant of variation k is also called the constant of proportionality y 1 and x 2 are called the means y 2 and x 1 are called the extremes

9. Section 4.1: Direct Variation Examples y varies directly as x 8.y= -45 when x = 33, find x when y = -15 8.y = 96 when x = 36, find x when y = 24

10. Section 4.1: Direct Variation y varies directly as the square of x 10.y = 32 when x = 4, find y when x = 10 11.y = 63 when x = 3, find y when x = 4

11. Section 4.1: Direct Variation Homework Practice Exercises: Pg. 147 #2-52 (even)