Transcript Parallel Lines and Transversals

Linear Functions
Students will be able to determine whether
or not a function is linear and be able to
write a linear function given a real world
situation.
Linear Functions
• When given a data set, we can determine
whether it is a linear or nonlinear function.
• We look at the rate of change. This is
found by dividing the change in the y or f(x)
by the change in the x.
change in y or f(x)
change in x
• If the rate of change is constant, then the
function is linear.
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Data Sets
• We need to find the change in f(x) and the
change in x.
1
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1
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1
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1
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x
-2
-1
0
1
2
y or f(x)
-5
-2
1
4
7
3
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3
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3
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3
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• The ratio is constant, so this is linear.
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Slope of a Line
• The ratio that represents the rate of change
is also called the slope of the line.
change in y or f(x)
 slope
change in x
• A set of data that has a constant rate of
change is a linear function. The slope of
that line is the rate and the function can be
graphed using those points and the slope
of the line.
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Solving Problems
• We can use this information about linear functions
to help us solve problems. For example:
• Joe sells tents at the Outdoor Store. He is paid $56
a day and gets a $10 commission on every tent he
sells. Write an equation that represents this, and
compute Joe’s salary for a day if he sells 3 tents.
x would represent the number of tents sold
y would represent Joe’s daily salary.
The equation would be: y  10 x  56
So Joe’s salary would be: 10  3  56  $ 86
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