Algebra 1

Direct and InverseVariations

Objective

Students will understand the difference between direct and inverse variation.

Students will compute both direct and inverse variation.

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.

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.

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

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.

Inverse Variation

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

x1y1 = x2y2

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

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

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.