Graphing on a Coordinate Plane

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What am I Learning Today?

• Graphing on a Coordinate Plane

How will I show that I learned it?
Locate and graph ordered pairs in Quadrant I
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Vocabulary

• Coordinate plane Formed by two number lines in a
  plane that intersect at right angles.
• Axes Two number lines in a coordinate plane.
  X-axis is horizontal and y-axis is vertical.
• Ordered pairs Gives the location of a point on a
  coordinate plane.
• Coordinate The numbers in an ordered pair.

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Questions Answers
How is an ordered pair written?
(x, y)
What does an ordered pair tell you?
The first number tells how far to move right
(positive) from the origin along the x-axis. The
second number tells how far to move up (positive)
from the origin along the y-axis.
Where is the origin located?
(0,0)
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Graphing Ordered Pairs Graph and label each
point on a coordinate grid. A. L (3, 5)
Start at (0, 0).
Move right 3 units.
6
L
Move up 5 units.
5
4
3
2
B. M (4, 0)
1
M
Start at (0, 0).
0
1 2 3 4 5 6
Move right 4 units.
Move up 0 units.
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Graphing Ordered Pairs Graph and label each point
on a coordinate grid. A. T (2, 6)
Start at (0, 0).
T
6
Move right 2 units.
5
Move up 6 units.
4
3
2
B. V (5, 0)
1
V
Start at (0, 0).
0
1 2 3 4 5 6
Move right 5 units.
Move up 0 units.
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Try These
Give the ordered pair for each point. 1. A 2.
B 3. C 4. D Graph and label each point on
a coordinate grid. 5. F(7, 2) 6. G(1, 7)
(4, 6)
G
(6, 1)
(1, 4)
F
(2, 1)
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Practice
http//www.thatquiz.org/tq-7/?-jc8-l5-n35-p2kc0
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What am I Learning Today?

• Patterns, Tables, and Functions

How will I show that I learned it?
Analyze and describe patterns arising from
mathematical rules, tables and graphs Identify an
equation based on a tables pattern and find the
missing values Represent an equation using
ordered pairs and translate onto a graph
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How do you solve with a Table?
First, start with an equation. y 3x Next,
create a table
INPUT (X) OUTPUT (Y)





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How do you solve with a Table?
y 3x Put numbers into the input side of the
table. We are going to INPUT (x value) each
number into the equation above to determine what
the OUTPUT (y value) will be. What is the
OUTPUT (y value) for the table?
INPUT (X) OUTPUT (Y)





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How do you solve with a Table?
y 7x Put numbers into the input side of the
table. We are going to INPUT (x value) each
number into the equation above to determine what
the OUTPUT (y value) will be. What is the
OUTPUT (y value) for the table?
INPUT (X) OUTPUT (Y)





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How do you solve with a Table?
y ½ x Put numbers into the input side of the
table. We are going to INPUT (x value) each
number into the equation above to determine what
the OUTPUT (y value) will be. What is the
OUTPUT (y value) for the table?
INPUT (X) OUTPUT (Y)





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Questions Answers
A rule that relates two quantities so that each
input value corresponds to exactly one output
value.
What is a function?
How do I find an equation for a table of values?

• Compare x and y values to find a pattern.
• Write an equation that fits every pair of values.

How do I find the missing values in a table?
Use substitution to solve for the missing value
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Writing Equations from Function Tables
Write an equation for a function that gives the
values in the table. Use the equation to find the
value of y for the indicated value of x.
x 3 4 5 6 7 10
y 13 16 19 22 25
y is 3 times x 4.
y 3x 4
y 3(10) 4
y 30 4 34
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Writing Equations from Function Tables
Write an equation for a function that gives the
values in the table. Use the equation to find the
value of y for the indicated value of x.
x 3 4 5 6 7 10
y 10 12 14 16 18
y is 2 times x 4.
y 2x 4
y 2(10) 4
y 20 4 24
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What am I Learning Today?

• Substitution

How will I show that I learned it?
Plug in numbers for letters.
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Questions Answers
Questions Notes
When you exchange a letter (variable) in an
equation for a number and then solve.
What is substitution?
y 6x Did you notice that we are using an x and
a y variable? That is because we are going to use
the x and the y numbers to graph them.
What kind of equation can we use?
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Questions Answers
Questions Notes
How do you solve a substitution problem?
Using y 6x, what is the value of x if y
42. Substitute 42 in for the y. It will look
like. 42 6x Thats a one step equation and we
know how to solve that. 42 6x 6 6 7 x
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Now, you practice. Using y 8x, what is the
value of x if y 56. y 8x 56 8x 8
8 7 x DID YOU GET IT RIGHT?
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Now you practice. Using y 3x, what is the
value of x if y 24. y 3x 24 3x 3
3 X 8 DID YOU GET IT RIGHT?
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Now you practice. Using y 9x, what is the
value of x if y 108. y 9x 108 9x 9 9 12
x DID YOU GET IT RIGHT?
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What am I Learning Today?

• Direct Variation

How will I show that I learned it?
Recognize direct variation and describe this
proportional relationship using an equation Graph
proportional relationships
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Questions Answers
Questions Notes
An equation where as 1 variable increases, the
other variable increases at the same rate. The
two quantities always have equivalent ratios.
(Like equivalent fractions)
What is direct variation?
In what 3 ways can direct variation be
represented?
Table, equation, and graph
A straight line through the point of origin (0,0)
What does direct variation look like on a graph?
Why do the direct variation equations have two
variables?
Since direct variations can be graphed, there to
be an x value and a y value for the equation so
we can graph it.
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Determine whether the values in the table
represent a direct variation. If so, write a
direct variation equation for the variation. If
not, explain.
x -1 1 2 2.5
y -4 4 8 10
0
0
Direct-Variation Equation
Direct Variation
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Determine whether the values in the table
represent a direct variation. If so, write a
direct variation equation for the variation. If
not, explain.
x 3 4 5 6
y 4.5 6 7.5 9
Direct Variation
Direct-Variation Equation
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Determine whether the values in the table
represent a direct variation. If so, write a
direct variation equation for the variation. If
not, explain.
x 1 2 3 4
y 4 6 8 10
The line did not go through the origin!
NOT Direct Variation
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Determine whether the values in the table
represent a direct variation. If so, write a
direct variation equation for the variation. If
not, explain.
x -2 -1 0 1
y 4 1 0 1
It is not linear!
NOT Direct Variation
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Finding the values and graphing using a direct
variation equation

• At a jumping contest, Evans frog jumped 60
  inches. Isabellas frog jumped 72 inches. Jakes
  frog jumped 78 inches. Use the equation y12x,
  where y is the number of inches and x is the
  number of feet, to find the missing values in the
  table.

Evans frog Isabellas frog Jakes frog
Inches (y) 60 72
Feet (x) 6 6.5
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Finding the values and graphing using a direct
variation equation

• There are 60 minutes in an hour. Find a missing
  values in the table using the direct variation
  equation y60x, where x is the number of hours
  and y is the number of minutes.

Hours (x) Minutes (y)
0
3
360
24
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Finding the values and graphing using a direct
variation equation

• Tyler rides his bike at a constant speed of 9mph.
  Complete the table using the equation y9x, where
  x is the number of hours and y is the number of
  miles he travels.

Hours (x) Miles (y)
1 9
1.5
3
45
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Create a table, write and equation and graph the
direct variation

• All spiders have 8 legs. Therefore, 2 spiders
  have 16 legs, 3 spiders have 24 legs, and so on.
• A rose bush grows 3 inches every 4 months. How
  many inches will it have grown in a year?
• Six packs of gum cost 2.00 each. At that rate,
  how much will 42 packs of gum cost?