Write linear equations that represent direct variation

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Presentation transcript:

Write linear equations that represent direct variation Goal: Write linear equations that represent direct variation Eligible Content: A1.2.2.1.1 / A1.2.2.1.2

Vocabulary Direct Variation - When two variables are related in such a way that the ratio of their values always remains the same. y = kx Constant of Variation – the relationship between the two variables k

In other words : Direct variation is when one variable is a multiple of the other variable. Equation looks like: y = kx k can be any number except 0. We call k the constant of variation.

Examples Find the constant of variation and the slope of each direct variation problem. 1. y = 2x 2. y = - ½ x m = - ½ k = - ½ m = 2 k = 2

Name the constant of variation for the equation Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. A. constant of variation: 4; slope: –4 B. constant of variation: 4; slope: 4 C. constant of variation: –4; slope: –4 D. constant of variation: slope:

Name the constant of variation for the equation Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. A. constant of variation: 3; slope: 3 B. constant of variation: slope: C. constant of variation: 0; slope: 0 D. constant of variation: –3; slope: –3

Examples The variables x and y vary directly. Use the given values to write an equation that relates x and y. x = 5 and y = 20 x = -3 and y = -30 x = 10 and y = 5 x = 35 and y = 7 x = 17 and y = 4.25 y = 4x y = 10x y = ½ x y = 1/5 x y = ¼ x

Suppose y varies directly as x, and y = 15 when x = 5 Suppose y varies directly as x, and y = 15 when x = 5. Write a direct variation equation that relates x and y. A. y = 3x B. y = 15x C. y = 5x D. y = 45x

Practice Worksheet – “3-4 Direct Variation” Complete part A

More Examples Assume the variables vary directly. Use an equation to find the value of y. If x = 4 when y = 12, find y when x = -2. If x = 1 when y = -7, find y when x = 3. If x = 12 when y = 2, find y when x = 18. If x = 3 when y = 36, find y when x = -4. y = -6 y = -21 y = 3 y = -48

Suppose y varies directly as x, and y = 15 when x = 5 Suppose y varies directly as x, and y = 15 when x = 5. Use the direct variation equation to find x when y = –45. A. –3 B. 9 C. –15 D. –5

More Practice Worksheet – “3-4 Direct Variation” Complete part B

Homework Pages 185-186 #10-15 #24-27