11.3 Direct and Inverse Variations Objectives: 1.Recognize direct variations 2.Recognize inverse...

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Transcript of 11.3 Direct and Inverse Variations Objectives: 1.Recognize direct variations 2.Recognize inverse...
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
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, LaLaLa
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, LaLaLa
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.