Graphing Functions with Ordered Pairs
Find four solutions of
.
x
Choose four values for . Then substitute each value into the equation to solve
for . There are many possible solutions. The solutions you find depend on
which values you choose.
y
x
2
Graphing Functions with Ordered Pairs
Choose four
x values and substitute them into
x
y
(x, y )
0
1
2
3
9
7
5
3
(0, 9)
(1, 7)
(2, 5)
(3, 3)
Sample Answer:
(0, 9), (1, 7), (2, 5), and (3, 3)
If 0 is the input  9 is the output.
If 1 is the input  7 is the output.
If 2 is the input  5 is the output.
If 3 is the input  3 is the output.
3
3
4
Graphing Functions with Ordered Pairs
Graph
by plotting ordered pairs.
First, find ordered pair solutions.
x
y
(x, y )
–1
0
1
2
–4
–3
–2
–1
(–1, –4)
(0, –3)
(1, –2)
(2, –1)
Four solutions are (–1,–4),
(0,–3), (1,–2), and (2,–1).
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Coordinate Plane
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7
Graphing Functions with Ordered Pairs
Plot these ordered pairs and draw a line through them.
Four solutions are (–1,–4),
(0,–3), (1,–2), and (2,–1).
Plot 2 points.
Now, draw a straight line between
the points
Extend your line well beyond the
two points.
Finally, check either of your last two
points.
Is it on your line?
Then, you’ve graphed correctly!
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9
Graphing Functions with Ordered Pairs
Graph y = 5 – x by plotting ordered pairs.
Answer:
10
Graphing Functions with xy Intercepts
x-intercept and the y-intercept of the line.
The graph crosses the x-axis at (–2, 0). The xintercept is –2. The graph crosses the y-axis at
(0, –2). The y-intercept is –2.
1. State the
Answer:
2. State the
–2; –2
x-intercept and the y-intercept of the line.
The graph does not cross the
-axis. There is no -intercept. The graph
crosses the -axis
at (0, 2). The -intercept is 2.
x
y
x
y
Answer: none; 2
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Graphing Functions with xy Intercepts
State the
x-intercept and the y-intercept of each line.
3.
Answer:
4.
1; 3
Answer:
–1; none
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Graphing Functions with xy Intercepts
5.Find the
.
x-intercept and the y-intercept
for the graph of
To find the
x-intercept,. let
Write the equation.
Replace
y with 0.
Simplify.
The
x-intercept is 4. So, the graph crosses the x-axis at (4, 0).
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Graphing Functions with xy Intercepts
5. To find the
y-intercept, let
.
Write the equation.
Replace
x with 0.
Simplify.
Divide each side by 2.
The
y-intercept is 2. So, the graph crosses the y-axis at (0, 2).
Answer:
x-intercept, 4; y-intercept, 2
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Graphing Functions with xy Intercepts
7. Graph
Step 1
The
using the
Find the
x-intercept.
x-intercept is 2, so the graph
passes through (2, 0).
x- and y-intercepts.
Write the equation.
Replace
y with 0.
Add 6 to each side.
Divide each side by 3.
Step 2
The
Find the
y-intercept.
y-intercept is –6, so the graph
passes through (0, –6).
Write the equation.
Replace
x with 0.
Simplify.
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Graphing Functions with xy Intercepts
7. The x-intercept is 2. So,
the graph crosses the
x-
axis at (2, 0).
The y-intercept is –6, so the
graph passes through (0, –
6).
Draw your line.
Check
Choose some
other point on the line and
determine whether its
ordered pair is a solution of
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17
Graphing Functions with xy Intercepts
8. Graph
using the
x- and y-intercepts.
Answer:
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Graphing Functions with xy Intercepts
9. Mrs. Jones has $300 for home repairs. A plumber charges her $50 an hour. The
equation
represents the amount of money left in her budget after
number of plumbing hours.
Use the intercepts to graph the equation.
x
Step 1
Find the
x-intercept.
9. Step 2 Find the
Write the equation.
Replace
y-intercept.
Write the equation.
y with 0.
Replace x with 0.
Subtract 300
from each side.
The
Divide each side by –50.
The
x-intercept is 6.
y-intercept is 300.
Reread the problem. Since the x-intercept
is 6, what does that actually mean?
The y-intercept is 300. What does that
actually mean?
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Graphing Functions with xy Intercepts
9. Answer:
Describe what the intercepts
mean.
Answer: The y-intercept
(0, 300)
shows how much money
Mrs. Jones has in her
budget before any work is
done. The x-intercept
(6, 0)
means that she can afford
only 6 hours of plumbing
repair.
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Graphing Functions with xy Intercepts
10. Suzanne has $125 to spend on
new shoes. The shoe store is having a
sale in which every pair of shoes is
priced at $25. The equation
represents the amount of money
Suzanne has left after purchasing
pairs of shoes.
Answer:
x
Use the intercepts to
graph the equation.
10. Describe what the intercepts mean.
y
Answer: The -intercept shows how
much money Suzanne has before buying
any shoes. The
x-intercept means that she
can afford only 5 pairs of shoes.
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Graphing Functions with xy Intercepts
11.
Graph
Note that
The
using the
x- and y-intercepts.
is the same as
y-intercept is –4, and there is no x-intercept.
Answer:
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Graphing Functions with xy Intercepts
12.
Graph
Note that
The
using the
x- and y-intercepts.
is the same as
x-intercept is 5, and there is no y-intercept.
Answer:
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Graphing Functions with xy Intercepts
Graph each equation using the
13.
Answer:
x- and y-intercepts.
14.
Answer:
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Make Your Own Function
Rewrite your data in set notation*
* Set notation lists data as ordered pairs.
* Example: { (2,8), (-8,7), (0,4) }
~ What is the independent variable?
~ Write only the domain of the data in set notation.
~ What is the dependent variable?
~ Write only the range of the data in set notation.
~ Does the data represent a function?
* Explain your answer.
'
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Make Your Own Function
Plot all ordered pairs, then connect each point from left to right.
~ When the line crosses the x-axis, what's the value of y?
~ What's the x-intercept?
~ When the line crosses the y-axis, what's the value of y?
~ What's the y-intercept?
~ What does the x-intercept mean?
~ What does the y-intercept mean?
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Coordinate Plane
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Coordinate Plane
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