Chapter 4: Systems of Equations

and InequalitiesSection 4.1: Direct Variation

Section 4.1: Direct Variation

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

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

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

Week Amount0 01 502 1003 1504 2005 250

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

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

Section 4.1: Direct Variation

• Examples• y varies directly as x6. 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

Section 4.1: Direct Variation

• If y varies directly as x, then for any two ordered pairs

(x1, y1) and (x2, y2), 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• y1 and x2 are called the means• y2 and x1 are called the extremes

Section 4.1: Direct Variation

• Examples• y varies directly as x8. y= -45 when x = 33, find x when y = -15

9. y = 96 when x = 36, find x when y = 24

Section 4.1: Direct Variation

• y varies directly as the square of x10.y = 32 when x = 4, find y when x = 10

11.y = 63 when x = 3, find y when x = 4

Section 4.1: Direct Variation

• Homework• Practice Exercises: Pg. 147 #2-52 (even)