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Objective - To write and to graph linear equations that describe dependent relationships

Objective - To write and to graph linear equations that describe dependent relationships. Let n = # of triangles. Independent. Dependent. p. n. Let p = the perimeter of each figure . 1. 3. A) Find an equation that describes p in terms of n. 2. 4. p = n + 2. 3. 5.

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Objective - To write and to graph linear equations that describe dependent relationships

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  1. Objective - To write and to graph linear equations that describe dependent relationships Let n =# of triangles Independent Dependent p n Let p = the perimeter of each figure 1 3 A) Find an equation that describes p in terms of n. 2 4 p = n + 2 3 5 B) Find the perimeter of 100 such triangles. 4 6 p = n + 2 5 7 p = 100 + 2 6 8 p = 102

  2. Let n =# of squares Let p = perimeter of figure Independent Dependent p n 1 4 A) Find an equation that describes p in terms of n. 2 6 p = 2n + 2 3 8 B) Find the perimeter of 405 such squares. 4 10 p = 2n + 2 5 12 p = 2(405) + 2 6 14 p = 812

  3. Let n =# of hexagons Independent Dependent Let p = perimeter of figure p n 1 6 A) Find an equation that describes p in terms of n. 4 2 10 4 p = 4n + 2 3 14 4 B) Find the perimeter of 322 such hexagons. 4 18 4 p = 4n + 2 5 22 4 p = 4(322) + 2 6 26 p = 1290

  4. Let n =# of triangles Independent Dependent p n Let p = the perimeter of each figure 1 3 A) Find an equation that describes p in terms of n. 2 4 p = n + 2 3 5 B) Find the perimeter of 100 such triangles. 4 6 p = n + 2 5 7 p = 100 + 2 6 8 p = 102

  5. Let n =# of squares Let p = perimeter of figure Independent Dependent p n 1 4 A) Find an equation that describes p in terms of n. 2 6 p = 2n + 2 3 8 B) Find the perimeter of 405 such squares. 4 10 p = 2n + 2 5 12 p = 2(405) + 2 6 14 p = 812

  6. Instance: 1 2 3 4 # of Squares: 5 9 13 17 Let n = Instance or Design # S n Let S = Number of Squares Used 1 5 2 9 3 13 4 17 5 21 4 Write an equation that describes S in terms of n. 4 4 S = ___n + ___ 4 1 4 Change Start Value

  7. This chart shows the price of sliced fruit platters. 1) How much would a 6 lb. platter cost? $8.10 + 1.50 = $ 9.60 1.50 1.50 2) Write an equation for the cost of a platter that weighs w lbs. 1.50 1.50 Let p = price of platter 3) How much would a 10 lb. platter cost? p = 1.50 w + 0.60 p = 1.50 w + 0.60 Change Start Value p = 1.50 ( 10 ) + 0.60 p = 15.00 + 0.60 = $15.60

  8. Complete the x-y chart and use it to write a linear equation for y in terms of x. x x y y 1) 2) 0 1 2 3 4 5 2 5 8 __ __ __ 0 1 2 3 4 5 7 3 -1 __ __ __ 3 -4 3 -4 3 -4 11 -5 3 -4 14 -9 3 -4 17 -13 3 2 -4 7 y = ___x + ___ y = ___x + ___ Change Change Start Value Start Value

  9. Complete the x-y chart and use it to write a linear equation for y in terms of x. x x y y 3) 4) -3 -2 -1 0 1 2 5 7 9 __ __ __ -14 -11 -8 __ __ __ -3 -2 -1 0 1 2 2 3 2 3 2 3 11 -5 2 3 13 -2 2 3 15 1 2 11 3 -5 y = ___x + ___ y = ___x + ___ Change Change Start Value Start Value

  10. A taxi cab charges a flat rate of $2.50 and 15 c per mile. Write a linear equation for the charge in terms of the number of miles driven. Let C = charge in dollars Let m =# of miles driven C = 2.50 + 0.15 m Start Value Change

  11. A phone company charges $17.50 per month and 12 c for each additional minute . Write a linear equation for the charge in terms of the number of minutes. Let C = charge in dollars Let m =# of minutes C = 17.50 + 0.12 m Start Value Change

  12. Jason has $60 and is spending $11 a day. a) Define variables. Which is dependent? b) Write an equation to describe the money Jason has in terms of the days. c) Make an x-y chart and graph.

  13. Jason has $60 and is spending $11 a day. b) y = 60 - 11x a) Let x =# of days Let y = Jason’s money y depends on x Line is decreasing 60 50 40 30 20 10 c) x y Line is discrete 0 1 2 3 4 5 60 49 38 27 16 5 Jason’s Money ($) 0 1 2 3 4 5 6 # Days

  14. A car’s fuel tank is filled at a rate of 1.6 gal/min. The tank held 5 gallons of gas before refueling. a) Define variables. Which is dependent? b) Write an equation to describe the volume of gas in the tank in terms of time. c) Make an x-y chart and graph.

  15. A car’s fuel tank is filled at a rate of 1.6 gal/min. The tank held 5 gallons of gas before refueling. a) Let m =# of minutes Let V = Volume of gas in tank V depends on m b) V = 5 + 1.6m c) 30 25 20 15 10 5 m V Line is increasing 0 2 4 6 8 10 5 8.2 11.4 14.6 17.8 21 Volume of gas in tank Line is continuous 0 2 4 6 8 10 12 # minutes

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