Writing Equations For Proportions Day 6.

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Writing Equations For Proportions Day 6

The constant of proportionality and the unit rate are equivalent. We can use the constant of proportionality to help write equations using proportional relationships. By transforming the equation from: to y = kx, we can write an equation that can be applied to various situations. *Remember: x is the independent variable and y is the dependent variable. This means that a change in x will effect y.

EXAMPLE You are buying Jersey Tomatoes for a cost of 2 pounds for $3.98. Write an equation to represent the proportional relationship. Let c = cost p = pounds Determine the unit rate: k = $1.99 per pound Write an equation to relate the two quantities: c = kp c = 1.99p ×

TRY THIS: At the candy store, you purchase 5 lbs for $22.45. Write an equation to represent the proportional relationship. Let c = cost p = pounds Determine the unit rate: k = $4.49 per pound Write an equation to relate the two quantities: c = kp c = 4.49p Click Click

TRY THIS: Write an equation to represent the proportional relationship shown in the table. Let g = gallons m = miles m = 24.7g Gallons 10 15 20 25 Miles 247 370.5 494 617.5 Click

Write an equation that represents the proportional relationship. 55 Write an equation that represents the proportional relationship. The total cost (c) of grapes for $1.40 per pound(p) A c = 1.4p B p = 1.4c Answer: A

Write an equation that represents the proportional relationship. 56 Write an equation that represents the proportional relationship. Shirts 5 15 25 35 Cost $57.50 $172.50 $287.50 $402.50 A s = 11.5c B c = 11.5s C c = 0.09s D s = 0.09c Answer: k = c/s = 57.50/5 = 11.50/1 B

Write an equation that represents the proportional relationship. 57 Write an equation that represents the proportional relationship. 0 1 2 3 4 5 6 7 8 9 10 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 A B C D Answer: A

Write an equation that represents the proportional relationship. 58 Write an equation that represents the proportional relationship. You are ordering new menus for your restaurant. You pay $362.50 for 50 menus. A c = 0.14m B m = 7.25c C m = 0.14c D c = 7.25m Answer: k = c/s = 362.50/50 = 7.25/1 D

Write an equation that represents the proportional relationship. 59 Write an equation that represents the proportional relationship. Days, d 2 3 4 5 Hours, h 17 25.5 34 42.5 A d = 8.5h B C D h = 8.5d Answer: k = h/d=17/2 = 8.5/1 D