Algebra 1 Direct and Inverse Variations Objective Students will understand the difference between...

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Algebra 1 Direct and Inverse Variations

Transcript of Algebra 1 Direct and Inverse Variations Objective Students will understand the difference between...

Page 1: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

Algebra 1

Direct and InverseVariations

Page 2: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

Objective

Students will understand the difference between direct and inverse variation.

Students will compute both direct and inverse variation.

Page 3: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

Direct Variation

When we talk about a direct variation, we are talking about a relationship where as x increases, y increases at a CONSTANT RATE.

Page 4: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

The price of hot dogs varies directly with the number of hotdogs you buy

You buy hotdogs. x represents the number of hotdogs you buy.

y represents the price you pay.

y = kx Let’s figure out k, the price per hotdog. Suppose that when you buy 7 hotdogs, it costs $21.

Plug that information into the model to solve for k.

y = kx21 = k(7) Now divide both sides by 7 to solve for k. 7 7

k = 3 The price per hotdog is $3.

y = 3x You could use this model to find the price (y) for any number of hotdogs (x) you buy.

Page 5: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

x (number of hotdogs)

y (price)

y = 3x

(1,3) When you buy 1 hotdog, you pay $3..(2,6) When you buy 2 hotdogs, you pay $6

.(3,9) When you buy 3 hotdogs, you pay $9

.(0,0) When you buy 0 hotdogs, you pay $0

Page 6: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

Inverse Variation

Inverse is very similar to direct, but in an inverse relationship as one value goes up, the other goes down. There is not necessarily a constant rate.

Page 7: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

Inverse Variation

With Direct variation we Divide our x’s and y’s. In Inverse variation we will Multiply them.

x1y1 = x2y2

Page 8: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

Inverse Variation

If y varies inversely with x and y = 12 when x = 2, find y when x = 8.

x1y1 = x2y2

2(12) = 8y 24 = 8y y = 3

Page 9: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

Inverse VariationIf y varies inversely as x and x = 18 when y = 6, find y when x = 8.

18(6) = 8y 108 = 8y y = 13.5

Page 10: Algebra 1 Direct and Inverse Variations Objective  Students will understand the difference between direct and inverse variation.  Students will compute.

Notebook Quiz Please take out a sheet of paper

and put the proper school heading on the upper left of the paper.

You may use your notebook and notes for this quiz.