Direct & Inverse Variations

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What You Will Learn Recognize and solve direct and joint variation problems Recognize and solve inverse variation problems.

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Presentation transcript:

Direct & Inverse Variations Sections 2-5 & 8-1

I can recognize and solve direct variation word problems. Objectives I can recognize and solve direct variation word problems. I can recognize and solve inverse variation word problems

As one variable increases, the other must also increase ( up, up) Direct Variation As one variable increases, the other must also increase ( up, up) OR As one variable decreases, the other variable must also decrease. (down, down)

Real life? With a shoulder partner take a few minutes to brainstorm real life examples of direct variation. Write them down. Food intake/weight Exercise/weight loss Study time/ grades Hourly rate/paycheck size Stress level/blood pressure Recipes Paint Mixtures Drug Manufacturing

Direct Variation k is the constant of variation the graph must go through the origin (0,0) and must be linear!!

K: Constant of Variation What does K really represent in direct variation??

Direct Variation Ex 1)If y varies directly as x and y = 12 when x = 3, find y when x = 10.

FIRST: Find your data points! Solving Method #1 FIRST: Find your data points! (x,y) NEXT: Solve for k & write your equation LAST: use your “unknown” data point to solve for the missing variable.

FIRST: Find your data points! Solving Method #2 FIRST: Find your data points! (x,y) NEXT: substitute your values correctly LAST: cross multiply to solve for missing variable.

What did we do? EITHER ONE WILL WORK!! ITS YOUR CHOICE! FIRST: Find your data points! (x,y) NEXT: Solve for k & write your equation LAST: use your “unknown” data point to solve for the missing variable. EITHER ONE WILL WORK!! ITS YOUR CHOICE! FIRST: Find your data points! (x,y) NEXT: substitute your values correctly LAST: cross multiply to solve for missing variable.

Direct Variation Application Ex: In scuba diving the time (t) it takes a diver to ascend safely to the surface varies directly with the depth (d) of the dive. It takes a minimum of 3 minutes from a safe ascent from 12 feet. Write an equation that relates depth (d) and time (t). Then determine the minimum time for a safe ascent from 1000 feet?

Your TURN #1 on Homework Find y when x = 6, if y varies directly as x and y = 8 when x = 2.

As one variable increases, the other decreases. (or vice versa) Inverse Variation As one variable increases, the other decreases. (or vice versa)

Inverse Variation This is a NON-LINEAR function (it doesn’t look like y=mx+b) It doesn’t even get close to (0, 0) k is still the constant of variation

Real life? Driving speed and time With a shoulder partner take a few minutes to brainstorm real life examples of inverse variation. Write them down. Driving speed and time Driving speed and gallons of gas in tank Pressure versus Volume Water Depth versus Time of dive

Inverse Variation Ex 3) Find y when x = 15, if y varies inversely as x and when y = 12, x = 10.

Solving Inverse Variation FIRST: Find your data points! (x,y) NEXT: Find the missing constant, k,by using the full set of data given LAST: Using the formula and constant, k, find the missing value in the problem

FIRST: Find your data points! Method #2 FIRST: Find your data points! (x,y) NEXT: substitute your values correctly LAST: use algebra to solve for missing variable.

What did we do? EITHER ONE WILL WORK!! ITS YOUR CHOICE! FIRST: Find your data points! (x,y) NEXT: Find the missing constant, k,by using the full set of data given LAST: Using the formula and constant, k, find the missing value in the problem FIRST: Find your data points! (x,y) NEXT: substitute your values correctly LAST: use algebra to solve for missing variable. EITHER ONE WILL WORK!! ITS YOUR CHOICE!

Inverse Variation Application Ex:The intensity of a light “I” received from a source varies inversely with the distance “d” from the source. If the light intensity is 10 ft-candles at 21 feet, what is the light intensity at 12 feet? Write your equation first.

Your TURN #2 on Homework Find x when y = 5, if y varies inversely as x and x = 6 when y = -18.

½ Sheet Data Examine the data that you have comparing two variables. Determine if the data varies directly or inversely or neither. After determining the type of variation, find the constant of variation and answer the question.

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Direct vs. Inverse Variation

Homework WS 1-3 Quiz next class on Parent Functions