1/16/13 Warm-Up Convert to y = mx+b  solve for y! 3x + 2y = 12

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Presentation transcript:

1/16/13 Warm-Up Convert to y = mx+b  solve for y! 3x + 2y = 12 -3x -3x 2y = -3x + 12 2 2 2 EQ: How do I find the rate of change of a linear function?

1/16/13 Opening CCGPS Standard: Objectives: Slope as rate of change SWBAT find the slope from a graph SWBAT define slope as the rate of change Use catalyst as an anticipation question. EQ: How do I find the rate of change of a linear function?

rise run x 1 free-response HOW When reading a graph, the slope is the _____________ over the _____________. This tells you how much the total goes up each time the ____ goes up by ____. Questions about this topic are usually ___________________, so you need to learn ______ to answer these questions. rise run x 1 free-response HOW EQ: How do I find the rate of change of a linear function?

Example 1 (Hours) 1. What is the slope of the line? rise: _______ m: _____ run: _______ 2. What is the meaning of the slope? The ____________ goes up/down by ___________ each ______. (Miles) 10 miles 10 1 hour distance 10 miles hour (Hours)

Example 1 (Hours) 3. What is the y-intercept? ____________ b: _____ 4. What is the meaning of the y-intercept? The initial _____________ was ______________. 5. What is the equation? ___________________ 10 miles 10 (Miles) distance 10 miles y = 10x + 10 (Hours)

Example 1 (Hours) 6. What is the total mileage after 6 hours? ________________ (Miles) 70 miles (Hours)

Practice 1 (Hours) 7. What is the slope of the line? rise: _______ m: _____ run: _______ 8. What is the meaning of the slope? The ____________ goes up/down by ___________ each ______. (Miles) 15 miles 15 1 hour distance 15 miles hour (Hours)

Practice 1 (Hours) 9. What is the y-intercept? ____________ b: _____ 10. What is the meaning of the y-intercept? The initial _____________ was ______________. 11. What is the equation? ___________________ 0 miles (Miles) distance 0 miles y = 15x + 0 (Hours)

Practice 1 (Hours) 12. What is the total mileage after 6 hours? ________________ (Miles) 90 miles (Hours)

Compare/Contrast 13. Which car is going faster? HOW do you know? ______________________________________________ 14. Which car started off farther ahead? HOW do you know? ________________________________________________ 15. Which car ended up going farther in the end? HOW do you know? _________________________________________________ The second car because the slope is bigger. The first car because the y-intercept is bigger. The second car because it went 90 miles in 6 hours, and the first car only went 70 miles.

Example 2 Time (Minutes) 1. What is the slope of the line? rise: _______ m: _____ run: _______ 2. What is the meaning of the slope? The ____________ goes up/down by ___________ each ______. -50 miles -25 Height (Yards) 2 hours height 25 yards minute Time (Minutes)

Example 2 Time (Minutes) 3. What is the y-intercept? ____________ b: _____ 4. What is the meaning of the y-intercept? The initial _____________ was ______________. 5. What is the equation? ___________________ 200 yards 200 Height (Yards) height 200 yards y = -25 x + 200 Time (Minutes)

Example 2 Time (Minutes) 6. What is the total height after 6 minutes? ________________ 50 yards Height (Yards) Time (Minutes)

Practice 2 Time (Minutes) 7. What is the slope of the line? rise: _______ m: _____ run: _______ 8. What is the meaning of the slope? The ____________ goes up/down by ___________ each ______. -25 miles Height (Yards) 4 hours -6.25 height -25/4 yards minute Time (Minutes)

Practice 2 Time (Minutes) 9. What is the y-intercept? ____________ b: _____ 10. What is the meaning of the y-intercept? The initial _____________ was ______________. 11. What is the equation? ___________________ 300 yards 300 Height (Yards) height 300 yards Time (Minutes)

Practice 2 Time (Minutes) 12. What is the total height after 6 minutes? ________________ about 263 yards Height (Yards) Time (Minutes)

Compare/Contrast 13. Which elevator is going faster? HOW do you know? _________________________________________________ 14. Which elevator started higher? HOW d you know? __________________________________________________ 15. Which elevator ended up arriving to the ground floor first? HOW do you know? ______________________________________________ The first elevator because the slope is bigger. The second elevator because the y-intercept is bigger. The first elevator because it will hit the ground floor at 8 minutes and the second elevator is still at 200 feet after 16 minutes.

Compare/Contrast 16. List BOTH reasons why this elevator arrived to the ground floor faster than the other elevator. a. _______________________________________________ b. ________________________________________________ The first elevator started off at a lower height. The first elevator moves faster than the second elevator.

1/16/13 Work Period Independent Practice handout – in groups Slope as rate of change Expectations: Remain seated at all times Follow the “10 Things” poster Raise your hand to ask a questions Work quietly and efficiently in groups Use catalyst as an anticipation question. EQ: How do I find the rate of change of a linear function?

1/16/13 Exit Slip Complete the Exit Slip handout individually Expectations: Do your best Show your work Keep your eyes on your own paper Use catalyst as an anticipation question. HWK: Finding slope worksheet #1-8. Show your work!