Page 64 - Math Course 1 (Book 2)

Linear Relationships

Non-proportional Relationships
Your Turn!

Examples Proportional Relationships

Write an equation in function notation for the Graph the data in the table. What conclusion can
relation graphed below. you make about the relationship between the
number of miles walked and the time spent
walking?

Make a table of ordered Hours 1 2 3 4 5
pairs for several points Miles 1.5 3 5.4 6 7.5
on the graph.
A. There is a linear relationship between the number
of miles walked and time spent walking.

B. There is a nonlinear relationship between the
number of miles walked and time spent walking.

+1 +1 +1 +1 C. There is not enough information on the table to
determine a relationship.
Hours 1 2 3 4 5 D. There is an inverse relationship between miles
Miles 1 4 7 10 13 walked and time spent walking.

+3 +3 +3 +3 Answer

The difference in the x values is 1, and the differ-
ence in the y values is 3. The difference in y values
is three times the difference of the x values. This B. Write an equation to describe the relationship
suggests that y = 3x. Check this equation. between hours and miles walked.

Check A. m = 3h
If x = 1, then y = 3(1) or 3. But the y value for x = 1 is B. m = 2h
1. This is a difference of –2. Try some other values C. m = 1.5h
in the domain to see if the same difference occurs. D. m = 1h

Answer
x 1 2 3 4 5
y is always 2
3x 3 6 9 12 15
less than 3x.
y 1 4 7 10 13 Non proportional Relationships
This pattern suggests that 2 should be subtracted Write an equation in function notation for the
from one side of the equation in order to correctly relation that is graphed.
describe the relation. Check y = 3x – 2.
A. f(x) = x + 2
x 1 2 3 4 5
B. f(x) = 2x
3x 3 6 9 12 15 C. f(x) = 2x + 2
y 1 4 7 10 13 D. f(x) = 2x + 1
If x = 2, then y = 3(2) – 2 or 4. Answer
If x = 3, then y = 3(3) – 2 or 7.

y = 3x – 2 correctly describes
this relation. Since the relation is
Answer also a function, we can write the
equation in function notation as
f (x) = 3x – 2.

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