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11.3 Direct and Inverse Variations Objectives: 1.Recognize direct variations 2.Recognize inverse variations 3.Write direct and inverse variation equations 4.Graph direct and inverse variation equations 5.Use direct and inverse variations in real life Vocabulary: direct variation, inverse variation, constant of variation

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eat food – weight gain DirdirsInninns

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exercise – weight gain Dirdirs eat food – weight gain Inninns

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study time - grades Dirdirs eat food – weight gain Inninns exercise – weight gain

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speed – wind resistance Dirdirs eat food – weight gain study time - grades Inninns exercise – weight gain

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speed – gas mileage Dirdirs eat food – weight gain study time – grades speed – wind resistance Inninns exercise – weight gain

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temperature - life of an ice cube Dirdirs eat food – weight gain study time – grades speed – wind resistance Inninns exercise – weight gain speed – gas mileage

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volume - distance away Dirdirs eat food – weight gain study time – grades speed – wind resistance Inninns exercise – weight gain speed – gas mileage temp. - life of an ice cube

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Thermostat setting - gas bill (winter) Dirdirs eat food – weight gain study time – grades speed – wind resistance Inninns exercise – weight gain speed – gas mileage temp. - life of an ice cube volume - distance away

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thermostat setting- electric bill (summer) Dirdirs eat food – weight gain study time – grades speed – wind resistance thermostat - gas bill (w) Inninns exercise – weight gain speed – gas mileage temp. - life of an ice cube volume - distance away

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work hours - free time hours Dirdirs eat food – weight gain study time – grades speed – wind resistance thermostat - gas bill (w) Inninns exercise – weight gain speed – gas mileage temp. - life of an ice cube volume - distance away thermostat - electric bill (s)

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work hours - spending money Dirdirs eat food – weight gain study time – grades speed – wind resistance thermostat - gas bill (w) Inninns exercise – weight gain speed – gas mileage temp. - life of an ice cube volume - distance away thermostat - electric bill (s) work hours - free time hours

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days between shower - # of friends Dirdirs eat food – weight gain study time – grades speed – wind resistance thermostat - gas bill (w) work hours - spending $ Inninns exercise – weight gain speed – gas mileage temp. - life of an ice cube volume - distance away thermostat - electric bill (s) work hours - free time hours

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make some up Dirdirs eat food – weight gain study time – grades speed – wind resistance thermostat - gas bill (w) work hours - spending $ Inninns exercise – weight gain speed – gas mileage temp. - life of an ice cube volume - distance away thermostat - electric bill (s) work hours - free time hours shower cycle - # of friends

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Variations Dirdirs eat food – weight gain study time – grades speed – wind resistance thermostat - gas bill (w) work hours - spending $ Inninns exercise – weight gain speed – gas mileage temp. - life of an ice cube volume - distance away thermostat - electric bill (s) work hours - free time hours shower cycle - # of friends

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Direct Variation – as one variable increases or decreases, the other variable does the same Inverse Variation – as variable increases or decreases, the other variable does the opposite

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Writing equations of variations: 1.Determine if direct or inverse 2.Plug in x and y to find the constant k 3.Write the equation with x and y When x is 3, y is 12. Find the equation that relates x and y directly.

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Writing equations of variations: 1.Determine if direct or inverse 2.Plug in x and y to find the constant k 3.Write the equation with x and y When x is 4, y is 32. Find the equation that relates x and y directly.

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Writing equations of variations: 1.Determine if direct or inverse 2.Plug in x and y to find the constant k 3.Write the equation with x and y When x is 45, y is 81. Find the equation that relates x and y directly.

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Writing equations of variations: 1.Determine if direct or inverse 2.Plug in x and y to find the constant k 3.Write the equation with x and y When x is 3, y is 12. Find the equation that relates x and y inversely.

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Writing equations of variations: 1.Determine if direct or inverse 2.Plug in x and y to find the constant k 3.Write the equation with x and y When x is 2, y is 5. Find the equation that relates x and y inversely.

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Writing equations of variations: 1.Determine if direct or inverse 2.Plug in x and y to find the constant k 3.Write the equation with x and y When x is 30, y is 7.5. Find the equation that relates x and y inversely.

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Writing equations of variations: 1.Determine if direct or inverse 2.Plug in x and y to find the constant k 3.Write the equation with x and y Write an equation that relates these variables. x1234 y12643

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Writing equations of variations: 1.Determine if direct or inverse 2.Plug in x and y to find the constant k 3.Write the equation with x and y Write an equation that relates these variables. x1234 y6121824

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Graph the variation: 1.Solve for y 2.Make a table and pick some x’s 3.Plug x’s in and find y’s 4.Plot points 5.Connect the dots, La-La-La

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Graph the variation: 1.Solve for y 2.Make a table and pick some x’s 3.Plug x’s in and find y’s 4.Plot points 5.Connect the dots, La-La-La

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The area covered by a truckload of mulch and the depth of the mulch are inversely related. A load covers an area of 325 ft 2 six inches deep. Write a model relating the area and the mulch depth. Use the model to find the area covered by mulch 4 inches deep.

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Algebra 1 Assignment: 11.3 p659 #12-36 even, 37-42 11.1-3 Quiz tomorrow Progress Report signature Outside show is a poor substitute for inner worth. Aesop

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2.4 and10.2 Direct/Inverse/Joint Variation ©2001 by R. Villar All Rights Reserved.

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