Direct Variation4.6

3-9 odd, 12-22 even, 23-25, 29-34

#31 He was seized by the fidgets,

Grab ONE sheet of graph paper

Rate of ChangeAs 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

bxmybxmy

2

1

Direct VariationSome 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

axy

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=2y=2x

y-75x=0

Y

X

Graph then find when x=2y=-4x

y=.5x

Y

X

Find a, then graphy=2, and x=4

y=26, and x=-2

Y

X

Find a, then graph

y=-4, and x=-18

y=15, and x=-6Y

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

PracticeY

X

y=-4x+5

PracticeY

X

521

xy

PracticeY

X

754

xy

Y-interceptsFormulas 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 touchi.e. two lines that have identical slopes with different y-intercepts

PracticeY

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?

2011 :Erika2015 :Louise

tStS

PracticeY

X

December 1st is

6 weeks away

PracticeY

X

Homework

4.6 3-9 odd, 12-22 even, 23-25, 29-34