Meg, Emma, Caroline, Laura, Pitzer, Luke

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Presentation transcript:

Meg, Emma, Caroline, Laura, Pitzer, Luke Lesson 4.5 Meg, Emma, Caroline, Laura, Pitzer, Luke

Video http://www.yourteacher.com/how_to/writing_equations_of_lines/direct_variation.php

Direct Variation Notes Direct Variation- special type of linear relationship that can be written by the form y=kx Constant of variation- the k in the equation y=kx is the nonzero constant

Examples directions: tell whether each equation represents a direct variation. If so, identify the constant of variation. -3x+5y=0 Answer: Y=3/5x = The constant of variation is 3/5

Example 2x+y=10 Not a direct variation y=4x+9 Not a direct variation 2y=-8x y=-4x Constant of Variation:-4

Graphing To Graph: 1. Write a direct variation equation. 2. Choose values of x and generate ordered pairs. 3. Graph the points and connect.

Example X Y=6x (x,y) Y=6(0)=0 (0,0) 1 Y=6(1)=6 (1,6) 2 Y=6(2)=12 The three-toed sloth is an extremely slow animal. On the ground, it travels at a speed of about 6 feet per minute. Write a direct variation equation for the distance y a sloth will travel in x minutes. They graph. X Y=6x (x,y) Y=6(0)=0 (0,0) 1 Y=6(1)=6 (1,6) 2 Y=6(2)=12 (2,12)

Walk-through X 1 3 5 Y 6 18 30 Method 1: Y=6x: each y-value is six times the corresponding x-value Method 2: Put the pairs into fraction form: y/x 6/1=6, 18/3=6, 30/5=6

Examples Method1: y=x-4 Method2: -2/2=-1, 0/4=0, 4/8=1/2: not a direct variation Y=7x X 2 4 8 Y -2 Cameron earns $7 dollars per hour at her after school job. The total amount of her pay checks varies directly with the amount of time she works. Write a direct variation equation for the amount of money y that she earns for working x hours.