Slope and Rate of Change. Rates of change are seen everywhere.
9/9/2011 ©Evergreen Public Schools 2010 1 Rate Of Change Key Concepts : rate of change slope slope...
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9/9/2011 ©Evergreen Public Schools 2010 1 Rate Of Change Key Concepts: • rate of change • slope • slope formula
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Transcript of 9/9/2011 ©Evergreen Public Schools 2010 1 Rate Of Change Key Concepts : rate of change slope slope...
9/9/2011
©Evergreen Public Schools 2010
1
Rate Of Change
Key Concepts:• rate of change• slope• slope formula
©Evergreen Public Schools 2010
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LEQ 2
Check off what
you already know
how to do.
Check off what
you already know
how to do.
I can find
slope y-intercept
table
graph
equationsituation
©Evergreen Public Schools 2010
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LaunchLaunchLaunchLaunchGive an example of a rate.
Describe rate.
©Evergreen Public Schools 2010
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LaunchLaunchLaunchLaunchWe can say the rate of change is the
ratio of change in input to the change in output
change in inputchange in output
or vertical change
horizontal change
©Evergreen Public Schools 2010
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1. Describe the rate of change of g(x) in words.
2. How is that rate of change of g(x) shown in
– the picture?– the table?– the graph?
Input Output
1 52 93 13
Task One g(x) Sequence Task One g(x) Sequence
Find the equation g(x) = _____________
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Task One g(x) Sequence Task One g(x) Sequence
3. Find g(6) = _____ Explain how you found it.
4. g(9) = 37. Find g(10) = _____ Explain how you found it.
5. Find g(20) = _____ Explain how you found it.
©Evergreen Public Schools 2010
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Task Two Arithmetic Sequences
Task Two Arithmetic Sequences
Use another representation to verify your answers.
6. If q(4) = 12 and q(5) = 9, find q(6).
7. If k(3) = 20 and k(7) = 28, a) find k(11) b) find k(8)c) find k(16) Explain how you know.d) Find the rate of change of k(x).
Explain how you know.
True or False? Why?
k(7) + k(8) = k(15)
©Evergreen Public Schools 2010
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Task ThreeTask Three
8. r(x) is a linear function. The
point (x1 , y1) is one point on
the line. The point (x2 , y2) is
a second point on the line.
So, m(x1) = y1 and m(x2) =
y2, and your table would
look like this.
x y
x1 y1
x2 y2
Find the rate of change for the table.
©Evergreen Public Schools 2010
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DebriefDebrief
9. The rate of change is called the slope and is written with the letter, r.
Use your answer from #8
to write a formula for slope.
x yx1 y1
x2 y2
©Evergreen Public Schools 2010
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5
3
12
4
Did you hit the target? I can find the slope and
y-intercept of a linear function from a table, graph, equation and situation.
Rate your understanding of the target from 1 to 5.
5 is a bullseye!
©Evergreen Public Schools 2010
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PracticePractice
Practice 4.1A Rate of Change
