Direct Variation odd, even, 3-9 odd, even, 23-25, #31 He was seized by the fidgets, Grab ONE sheet of graph paper

Rate of Change As previously shown, rate of change is most easily identified as the slope of a line connecting two points This concept aids us in comparing two equations when using slope intercept form, especially when the y-intercept stays the same

Direct Variation Some equations exhibit direct variation  Direct variation means that the y variable has a direct relation to x i.e. no y-intercept  Follows the form  Where a is called the constant of variation

Graphing with Direct Variation To graph direct variation, we follow the same rules for slope intercept, except b=0  y=2x  y-intercept=0  Slope=2 Y X

Graph then find when x=2 y=2x y-75x=0 Y X

Graph then find when x=2 y=-4x y=.5x Y X

Find a, then graph y=2, and x=4 y=26, and x=-2 Y X

Find a, then graph y=-4, and x=-18 y=15, and x=-6 Y X

Practical Example  The number s of tablespoons of salt needed in a saltwater fish tank varies directly with the number w of gallons of water in the tank. A pet shop owner recommends adding 100 tablespoons to a 20 gallon tank.  Find the constant of variation for the example  How many tablespoons should be added for a 30 gallon tank?

Practical Example  An object that weighs 100 pounds on Earth would weigh just 6 pounds on Pluto. Assume that weight P on Pluto varies directly with the weight E on Earth.  Find the constant of variation for the example  How much would you weigh on Pluto?

Most Important Points 1. Two variables show direct variation when the y-intercept is 0 2. The constant of variation is an index of that variation which is also the slope of the line

Practice Y X y=-4x+5

Practice Y X

Practice Y X

Y-intercepts Formulas are useful because we’re able to see relationships that occur when we change components of the equations What happens when we begin to change the y-intercept? Graphy=2x+2y=2x-3 Y X

Parallel Lines How do we define parallel lines? Parallel: Two lines that will never touch i.e. two lines that have identical slopes with different y-intercepts

Practice Y X

Practical Example  Louise and Erika are trying to save money to buy matching winter coats. They both currently have $20 saved, but need to get a total of $95 to buy their coats by December first. They both make $40 per week. Louise saves $15 of her check for her coat. Erika only saves $11. Will they both make their goal?

Practice Y X December 1 st is 6 weeks away

Practice Y X

Homework odd, even, 23-25, odd, even, 23-25, 29-34