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Slopes and Lines Mr. Epstein

Slopes and Lines Mr. Epstein. Y. Y = mX + b. X. How to Get Your Dream Car!. In 3 years, do you want to buy this:. Or this?. Objectives for the Week Learn about the “slope” of a line Learn formulas for lines Learn properties of lines Learn how to solve problems involving lines

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Slopes and Lines Mr. Epstein

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  1. Slopes and LinesMr. Epstein Y Y = mX + b X

  2. How to Get Your Dream Car! In 3 years, do you want to buy this: Or this?

  3. Objectives for the Week Learn about the “slope” of a line Learn formulas for lines Learn properties of lines Learn how to solve problems involving lines Objectives for the Day – Learn about slope Activities for the Day Introduction to slopes: definitions and examples Work Sheets done in pairs If time, play “Who Wants to be a Millionaire” game Agenda

  4. Example: Save $10 a week Savings 40 30 1 $10 2 $20 3 $30 4 $40 . . 20 10 Week 1 2 3 4 Slope Definition: The change in Y divided by the change in X between 2 points.Note(s): Sometimes called: Rate of change or “rise over run”. Abbreviated using the letter “m”.

  5. Example: Save $10 a week Savings 30 ---------- = ---- = 10 (4-1) 3 m = change in y --------------------- = change in x (40-10) 40 30 20 10 Week 1 2 3 4 Slope Definition: The change in Y divided by the change in X between 2 points.Note(s): Sometimes called: Rate of change or “rise over run”. Abbreviated using the letter “m”.

  6. Example: Save $10 a week Savings y2 y1 30 ---------- = ---- = 10 (4-1) 3 m = change in y --------------------- = change in x (40-10) 40 P2=(4,40) x2 x2 x1 y2 30 20 10 Week 1 2 3 4 P1= (1,10) x1 y1 You can calculate the slope using two points, p1=(x1,y1) and p2=(x2,y2), using: m = y2 –y1 ----------- x2 – x1

  7. Example: Car value drops p1 = (2001,25000) p2 = (2006,15000) 15000 - 25000 m = ---------------------------- 2006 - 2001 = -10000 ------------- 5 = -2000 (car drops in value $2000/year) Value $25,000 $15,000 Year 2001 2006 You can calculate the slope using two points, p1=(x1,y1) and p2=(x2,y2), using: m = y2 –y1 ----------- x2 – x1

  8. There’s a challenge problem on the back if you get done with problems 1 & 2. But don’t worry if you don’t get to it! Both students in pair should complete and discuss problem 1 before moving to problem 2. You need to get done with problems 1 & 2! Raise your hand if you have a question! Pair Activity

  9. Who Wants to be a Millionaire?

  10. 10 $1 Million Question: How many different points are needed to define a line? 9 $500,000 8 $250,000 7 $100,000 6 $50,000 5 $25,000 4 $10,000 3 $5,000 2 $1,000 1 $100 50:50 B: What’s the point? A: 1 C: 2 D: 0

  11. 10 $1 Million Question: What is the slope of the following line: 9 $500,000 8 $250,000 7 $100,000 6 $50,000 5 $25,000 4 $10,000 P2=(3,3) 3 $5,000 2 $1,000 P1=(0,0) 1 $100 50:50 A: -1 B: 3 C: Is he really gonna give us $1,000,000? D: 1

  12. 10 $1 Million Question: Which way do lines with negative slope go when moving left to right? 9 $500,000 8 $250,000 7 $100,000 6 $50,000 5 $25,000 4 $10,000 3 $5,000 2 $1,000 1 $100 50:50 A: Up B: Not enough info D: Negative slopes don’t exist C: Down

  13. 10 $1 Million Question: What is the slope of the following vertical line? 9 $500,000 8 $250,000 7 $100,000 6 $50,000 5 $25,000 4 $10,000 3 $5,000 2 $1,000 1 $100 50:50 A: Need 2 points to solve B: undefined D: ∞ (infinity) C: 0

  14. 10 $1 Million Question: If p1=(1,3) and p2=(5,-5), what is the slope of the line connecting them? 9 $500,000 8 $250,000 7 $100,000 6 $50,000 5 $25,000 4 $10,000 3 $5,000 2 $1,000 1 $100 50:50 A: -1/2 B: -2 D: 2 C: -5/2

  15. Question: Which slope is the smallest? Hint: Pay attention to sign of slope! 10 $1 Million 9 $500,000 8 $250,000 7 $100,000 2 6 $50,000 5 $25,000 3 4 $10,000 3 $5,000 1 2 $1,000 1 $100 50:50 B: 3 A: 1 D: Can’t tell C: 2

  16. 10 $1 Million Question: The Storm Runner Roller Coaster drops 180 ft. If the horizontal distance from the peak to the base is 30 ft, what is the slope? (Hint:slope=change in y ÷ change in x. ) 9 $500,000 8 $250,000 7 $100,000 6 $50,000 5 $25,000 4 $10,000 3 $5,000 2 $1,000 1 $100 50:50 A: -6 B: 1/6 D: 180 C: -60

  17. 10 $1 Million Question: Which line has the greatest slope? 9 $500,000 8 $250,000 7 $100,000 6 $50,000 3 5 $25,000 2 4 $10,000 3 $5,000 1 2 $1,000 1 $100 50:50 A: 3 B: 2 D: All slopes are equal C: 1

  18. 10 $1 Million Question: As of Saturday, the Yankees record was 5 wins and 6 losses. If the games played is the X-axis (independent variable) and the wins is the Y-axis (dependent variable), what is the slope? 9 $500,000 8 $250,000 7 $100,000 6 $50,000 5 $25,000 4 $10,000 3 $5,000 2 $1,000 1 $100 50:50 B: 5/6 A: 5/11 D: -6/11 C: 11/5

  19. 10 $1 Million Question: For any point p1=(a,b), where a and b are real numbers such that a ≠ b, what is the slope between this point and the point p2=(b,a)? 9 $500,000 8 $250,000 7 $100,000 6 $50,000 5 $25,000 4 $10,000 3 $5,000 2 $1,000 NOTE: Slope = (b-a)/(a-b) = -1 1 $100 50:50 B: b/a A: -1 D: Not enough info C: a/b

  20. Congratulations! You’re NOT a Millionaire But, You have learned a lot about Slopes!!!!!

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