11.3 Direct and Inverse Variations Objectives: 1.Recognize direct variations 2.Recognize inverse variations 3.Write direct and inverse variation equations.

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

eat food – weight gain

Dirdirs Inninns

exercise – weight gain

Dirdirseat food – weight gain

Inninns

study time - grades


Inninnsexercise – weight gain

speed – wind resistance


study time - grades


speed – gas mileage


study time – grades



temperature - life of an ice cube






volume - distance away






temp. - life of an ice cube

Thermostat setting - gas bill (winter)








thermostat setting- electric bill (summer)




thermostat - gas bill (w)





work hours - free time hours









thermostat - electric bill (s)

work hours - spending money











days between shower - # of friends





work hours - spending $







make some up












shower cycle - # of friends

Variations












shower cycle - # of friends

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

kxy

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

kxy

xky

xk

y

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 yWhen x is 3, y is 12. Find the equation that relates x and y directly.

kxy

k312

k4

4xy

4xy





kxy

k432

k8

8xy

8xy





kxy

k4581

k59

59

xy

x59

y




3. Write the equation with x and yWhen x is 3, y is 12. Find the equation that relates x and y inversely.

kxy k123 k36

36xy x36

y




3. Write the equation with x and yWhen x is 2, y is 5. Find the equation that relates x and y inversely.

kxy k52 k10

10xy x10

y




3. Write the equation with x and yWhen x is 30, y is 7.5. Find the equation that relates x and y inversely.

kxy k7.530 k225

225xy x

225y




3. Write the equation with x and yWrite an equation that relates these variables.

12xy x12

y

x 1 2 3 4

y 12 6 4 3




3. Write the equation with x and yWrite an equation that relates these variables.

x 1 2 3 4

y 6 12 18 24

k616

xy

6xy

Graph the variation:

23

xy

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

Graph the variation:

4xy

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

The area covered by a truckload of mulch and the depth of the mulch are inversely related. A load covers an area of 325 ft2 six inches deep. Write a model relating the area and the mulch depth. 1950xy

2ft487.5

Use the model to find the area covered by mulch 4 inches deep.

Algebra 1

Assignment: 11.3 p659 #12-

36 even, 37-42 11.1-3 Quiz

tomorrow Progress Report

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Outside show is a poor substitute for inner worth.

Aesop

11.3 Direct and Inverse Variations Objectives: 1.Recognize direct variations 2.Recognize inverse variations 3.Write direct and inverse variation equations.

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