2.5N.notebook
September 23, 2011
Using the domain and range below, construct a relation that is not a function. Explain.
a
1
b
2
c
3
DIRECT VARIATION
Def: If y varies directly as x, then their
ratio is constant.
y = k or y = kx where k is a real #
x
What does this equation represent? What will it be when graphed?
a line through th
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2.5N.notebook
September 23, 2011
Example 1: Write an equation for a direct
variation that has (2,8) as a solution.
Graph the equation.
Practice: x & y vary directly. Write an equation that relates x and y. Find x when y = 4.
Given x = ­3 and y = 15
Example 2: Do the following tables
represent a direct variation? Explain. If
yes, write an equation.
x
y
x
y
.5
2
1
3
1
4
1.5
5
3
12
2
6
Practice: x varies directly with y. Complete the table below and write the
equation.
x
y
5
2
3
1.2
.4
?
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2.5N.notebook
September 23, 2011
Example 4: Hooke's Law states that the
distance d a spring stretches varies directly
with the force f that is applied to it.
a) Suppose a string stretches 15 inches when a 9 pound force is applied. Write an equation that relates d to f.
b) Predict the distance that the spring will
stretch when a force of 6 pounds is applied.
Practice: Hail 0.5 inch deep and weighing 1800 pounds covers a roof. The hail's weight w varies directly with its depth d. Write an equation that relates d and w. Then
predict the weight on the roof of hail that
is 1.75 inches deep.
Journal: Explain how you know x and y represent a direct variation.
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September 23, 2011
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