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Splash Screen

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Splash Screen Then/Now You recognized arithmetic sequences and related them to linear functions. (Lesson 3 5) Write an equation for a proportional relationship. – PowerPoint PPT presentation

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Title: Splash Screen


1
Splash Screen
2
Then/Now
You recognized arithmetic sequences and related
them to linear functions. (Lesson 35)
  • Write an equation for a proportional relationship.
  • Write a relationship for a nonproportional
    relationship.

3
Vocabulary
  • inductive reasoning

4
Concept
5
Example 1 A
Proportional Relationships
  • A. ENERGY The table shows the number of miles
    driven for each hour of driving.

Graph the data. What can you deduce from the
pattern about the relationship between the number
of hours driving h and the numbers of miles
driven m?
Answer There is a linear relationship between
hours of driving and the number of miles driven.
6
Example 1 B
Proportional Relationships
  • B. Write an equation to describe this
    relationship.

Look at the relationship between the domain and
the range to find a pattern that can be described
as an equation.
7
Example 1 B
Proportional Relationships
Since this is a linear relationship, the ratio of
the range values to the domain values is
constant. The difference of the values for h is
1, and the difference of the values for m is 50.
This suggests that m 50h. Check to see if this
equation is correct by substituting values of h
into the equation.
8
Example 1 B
Proportional Relationships
Check If h 1, then m 50(1) or 50.
If h 2, then m 50(2) or 100. If h 3,
then m 50(3) or 150. If h 4, then m 50(4)
or 200. The equation is correct.
Answer m 50h
9
Example 1 B
Proportional Relationships
  • C. Use this equation to predict the number of
    miles driven in 8 hours of driving.

m 50h Original equation m 50(8) Replace h
with 8. m 400 Simplify.
Answer 400 miles
10
Example 1 CYP A
A. Graph the data in the table. What conclusion
can you make about the relationship between the
number of miles walked and the time spent walking?
  1. There is a linear relationship between the number
    of miles walked and time spent walking.
  2. There is a nonlinear relationship between the
    number of miles walked and time spent walking.
  3. There is not enough information on the table to
    determine a relationship.
  4. There is an inverse relationship between miles
    walked and time spent walking.
  1. A
  2. B
  3. C
  4. D

11
Example 1 CYP B
B. Write an equation to describe the relationship
between hours and miles walked.
A. m 3h B. m 2h C. m 1.5h D. m 1h
  1. A
  2. B
  3. C
  4. D

12
Example 1 CYP C
C. Use the equation from part B to predict the
number of miles driven in 8 hours.
A. 12 miles B. 12.5 miles C. 14 miles D. 16 miles
  1. A
  2. B
  3. C
  4. D

13
Example 2
Nonproportional Relationships
  • Write an equation in function notation for the
    graph.

Understand You are asked to write an equation of
the relation that is graphed in function
notation. Plan Find the difference between the
x-values and the difference between the y-values.
14
Example 2
Nonproportional Relationships
Solve Select points from the graph and place them
in a table
  • The difference in the x values is 1, and the
    difference in the y values is 3. The difference
    in y values is three times the difference of the
    x values. This suggests that y 3x. Check this
    equation.

15
Example 2
Nonproportional Relationships
If x 1, then y 3(1) or 3. But the y value
for x 1 is 1. This is a difference of 2. Try
some other values in the domain to see if the
same difference occurs.
y is always 2 less than 3x.
16
Example 2
Nonproportional Relationships
  • This pattern suggests that 2 should be
    subtracted from one side of the equation in order
    to correctly describe the relation. Check y 3x
    2.

If x 2, then y 3(2) 2 or 4. If x 3, then
y 3(3) 2 or 7.
Answer y 3x 2 correctly describes this
relation. Since the relation is also a function,
we can write the equation in function notation as
f(x) 3x 2.
Check Compare the ordered pairs from the table
to the graph. The points correspond.
?
17
Example 2 CYP
Write an equation in function notation for the
relation that is graphed.
  1. A
  2. B
  3. C
  4. D

A. f(x) x 2 B. f(x) 2x C. f(x) 2x
2 D. f(x) 2x 1
18
End of the Lesson
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