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SWBAT… Write lines in slope-intercept form Monday, 1/11/09

SWBAT… Write lines in slope-intercept form Monday, 1/11/09. Agenda WU (5 min) 3 examples of slope as rate of change (10 min) Cornell notes on “slope-intercept form” (30 min) Warm-Up 1. Place “hw#1: Slope” in a pile on your desks 2. Complete vocabulary note card – “Slope”

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SWBAT… Write lines in slope-intercept form Monday, 1/11/09

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  1. SWBAT… Write lines in slope-intercept form Monday, 1/11/09 Agenda • WU (5 min) • 3 examples of slope as rate of change (10 min) • Cornell notes on “slope-intercept form” (30 min) Warm-Up 1. Place “hw#1: Slope” in a pile on your desks 2. Complete vocabulary note card – “Slope” 3. Start problems on back of agenda HW #2: Writing Equations in slope-intercept

  2. WARM-UP – ON THE BACK OF AGENDA!!! Frank had 5 gallons of gasoline in his bike.  After driving 100 miles, he had 3 gallons left.  • Find the slope of the line • What does this slope tell us?

  3. Slope as the rate of change a. Find the slope of the line     Slope = rise/run = -2/100 = -1/50 b.  What does this slope tell us? Since -1/50 = -0.02, we know that Frank’s bike is burning 0.02 gallons of gasoline for every mile that he travels.   (The negative value of the slope tells us that the amount of gasoline in the tank is decreasing.)

  4. Four students are renting a car for a road trip. The cost of renting the car is given by the function C = 12.5 + 21d, where C is the total cost for renting the car for d days. What does the slope of the function represent? • cost per day

  5. The cost of prints from an online photo processor is given by C(p) = 29.99 + 0.13p. $29.99 is the cost of membership, and p is the number of 4-inch by 6-inch prints. What does the slope represent? • cost per print • cost of the membership • cost of the membership and 1 print • number of prints

  6. Non-Linear Equations http://en.wikipedia.org/wiki/File:Graph_of_sliding_derivative_line.gif

  7. y-intercept slope Now look at the equation below…… When an equation is in slope-intercept form: y = mx + b 2 What is the slope? ____________ 1 What is the y-intercept? ____________

  8. Given y = ½x + ¾, what is the slope and the y-intercept? m = ½ b = ¾

  9. Given y = ½x – ¾, what is the slope and the y-intercept? m = ½ b = -¾

  10. Given y = -½x – ¾, what is the slope and the y-intercept? m = -½ b = -¾

  11. 1.) What is the slope? .102.) What is the meaning of the slope?3.) What is the y-intercept. b = 54.) What is the meaning of the y-intercept?5.) Write the equation of the line. y = .10x + 5

  12. y = mx + b • y = mx+ b is an equation that defines a line • A line has two characteristics • Points that fall on the line • Slope

  13. 1.) What is the slope? 2.) What is the meaning of the slope?3.) What is the y-intercept (write as an ordered pair) 4.) What is the meaning of the y-intercept?5.) Write the equation of the line (y = mx + b).

  14. Converting linear equations into Slope-Intercept Form 4 Examples

  15. Slope intercept form is: y = mx + b Our main goal is to get the y alone on one side of the equation

  16. Example 1 - convert into Slope-Intercept Form (divide both sides by 2 to get y alone) (now simplify all fractions) 2 1 What is the slope? _____ What is the y-intercept? ______

  17. *** Your turn – Example 2 – convert to Slope-Intercept Form*** -3y = -9x – 12 Step 1: divide both sides by -3 to get y alone Step 2: Simplify all fractions Step 3: Write your equation in y = mx + b What is the slope? ____________ What is the y-intercept? ____________

  18. -3-3 -3y = -9x – 12 -3-3 -3 *** Check Your Answer *** -3y = -9x – 12 (divide both sides by -3 to get y alone) (now simplify all fractions) y = 3x + 4 Wow, you’re good at this!! Slope = 3 Intercept = 4

  19. ***Example 3*** Convert to Slope-Intercept Form 21x – 7y =14 (subtract both sides by 21x) (now divide both sides by -7) -7y = -21x + 14 (simplify all fractions) y = 3x – 2 What is the slope? _________ What is the y-intercept? ________

  20. EXIT SLIP Convert to Slope-Intercept Form*** 2y + 26 = -6x Step 1: Subtract both sides by 26 Step 2: Divide both sides by 2 to get y by itself Step 3: Simplify all fractions What is the slope? ____________ What is the y-intercept? ____________

  21. *** Check Your Answer*** 2y + 26 = -6x (subtract both sides by 26) (now divide both sides by 2 2y = -6x – 26 (simplify all fractions) y = -3x – 13 You are a math wizard!

  22. In the standard (x, y) coordinate plane, what is the slope of the line given by the equation 5x – 4y = 3?

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