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

Dirdirseat food – weight gain

Inninnsexercise – weight gain

speed – wind resistance

Dirdirseat food – weight gain

study time - grades

Inninnsexercise – weight gain

speed – gas mileage

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

Inninnsexercise – weight gain

temperature - life of an ice cube

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

Inninnsexercise – weight gain

speed – gas mileage

volume - distance away

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

Inninnsexercise – weight gain

speed – gas mileage

temp. - life of an ice cube

Thermostat setting - gas bill (winter)

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

Inninnsexercise – weight gain

speed – gas mileage

temp. - life of an ice cube

volume - distance away

thermostat setting- electric bill (summer)

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

thermostat - gas bill (w)

Inninnsexercise – weight gain

speed – gas mileage

temp. - life of an ice cube

volume - distance away

work hours - free time hours

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

thermostat - gas bill (w)

Inninnsexercise – weight gain

speed – gas mileage

temp. - life of an ice cube

volume - distance away

thermostat - electric bill (s)

work hours - spending money

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

thermostat - gas bill (w)

Inninnsexercise – weight gain

speed – gas mileage

temp. - life of an ice cube

volume - distance away

thermostat - electric bill (s)

work hours - free time hours

days between shower - # of friends

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

thermostat - gas bill (w)

work hours - spending $

Inninnsexercise – weight gain

speed – gas mileage

temp. - life of an ice cube

volume - distance away

thermostat - electric bill (s)

work hours - free time hours

make some up

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

thermostat - gas bill (w)

work hours - spending $

Inninnsexercise – 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

Variations

Dirdirseat food – weight gain

study time – grades

speed – wind resistance

thermostat - gas bill (w)

work hours - spending $

Inninnsexercise – 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

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

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 4, y is 32. Find the equation that relates x and y directly.

kxy

k432

k8

8xy

8xy

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 45, y is 81. Find the equation that relates x and y directly.

kxy

k4581

k59

59

xy

x59

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 inversely.

kxy k123 k36

36xy x36

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 2, y is 5. Find the equation that relates x and y inversely.

kxy k52 k10

10xy x10

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 30, y is 7.5. Find the equation that relates x and y inversely.

kxy k7.530 k225

225xy x

225y

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 yWrite an equation that relates these variables.

12xy x12

y

x 1 2 3 4

y 12 6 4 3

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 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