Bellwork

1. Bellwork No Clickers • Rewrite the following equations to solve for y • 4x-2y=-8 • -9x+3y=21 • You are traveling by bus. After 4.5 hours the bus has traveled 234 miles. Use the formula d=rt to find the average rate of speed of the bus

2. Bellwork Solution • Rewrite the following equations to solve for y • 4x-2y=-8

3. Bellwork Solution • Rewrite the following equations to solve for y • -9x+3y=21

4. Bellwork Solution You are traveling by bus. After 4.5 hours the bus has traveled 234 miles. Use the formula d=rt to find the average rate of speed of the bus

5. Direct Variation Section 4.6

6. Yesterday Review Rate of Change

7. 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

8. 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

9. Practice y=-4x y=2x y=.5x y-75x=0

10. Y X 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

11. Steps for Lines using Slope Intercept Form • Draw axes • Use a Straightedge • Label X, Y • Include arrowheads • Determine a Scale • Label several points • Plot two points • Point #1: y-intercept • Point #2: Using slope count up or down and over • Draw line • Use a Straightedge • Connect the two points • Draw Arrowheads

12. 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?

13. Homework 4.6 1, 2, 3-9 odd, 10-22 even, 23-28, 40-45, 48-62 even & on a separate sheet of paper, write 5 word problems that utilize the concept of direct variation.

14. 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?

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

16. Y X Practice y=-4x+5

17. Y X Practice

18. Y X Practice

19. 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? Graph y=2x+2 y=2x-3

20. 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

21. Y X Practice

22. 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?

23. Y X Practice December 1st is 6 weeks away

24. Y X Practice