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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
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.
Questions
How is an
ordered pair
written?
What does an
ordered pair
tell you?
Answers
(x, y)
The first number tells how far to move
right (positive) from the origin along the xaxis.
The second number tells how far to move
up (positive) from the origin along the yaxis.
Where is the
origin located?
(0,0)
Graphing Ordered Pairs
Graph and label each point on a coordinate grid.
A. L (3, 5)
Start at (0, 0).
Move right 3 units.
Move up 5 units.
6
5
L
4
3
B. M (4, 0)
Start at (0, 0).
Move right 4 units.
Move up 0 units.
2
1
0
M
1
2
3
4
5
6
Graphing Ordered Pairs
Graph and label each point on a coordinate grid.
A. T (2, 6)
Start at (0, 0).
Move right 2 units.
Move up 6 units.
B. V (5, 0)
Start at (0, 0).
Move right 5 units.
Move up 0 units.
T
6
5
4
3
2
1
0
V
1
2
3
4
5
6
Try These
Give the ordered pair for each point.
1. A
(4, 6)
2. B
(6, 1)
3. C
(1, 4)
4. D
G
F
(2, 1)
Graph and label each point on a coordinate grid.
5. F(7, 2)
6. G(1, 7)
Practice
http://www.thatquiz.org/tq-7/?-jc8-l5-n35-p2kc0
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 table’s pattern
and find the missing values
Represent an equation using ordered pairs
and translate onto a graph
How do you solve with a Table?
First, start with an equation.
y = 3x
Next, create a table
INPUT (X)
OUTPUT (Y)
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.
INPUT (X)
What is the OUTPUT
(y value) for the table?
OUTPUT (Y)
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.
INPUT (X)
What is the OUTPUT
(y value) for the table?
OUTPUT (Y)
How do you solve with a Table?
y=½x
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.
INPUT (X)
What is the OUTPUT
(y value) for the table?
OUTPUT (Y)
What am I Learning Today?
Substitution
How will I show that I learned it?
Plug in numbers for letters.
Questions
Answers
When you exchange a letter (variable) in an equation
What is
substitution? for a number and then solve.
What kind of
equation can we
use?
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.
Questions
How do you
solve a
substitution
problem?
Answers
Using y = 6x, what is the value of x if y = 42.
Substitute 42 in for the y. It will look like.
42 = 6x
That’s a one step equation and we know how
to solve that.
42 = 6x
6
6
7=x
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?
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?
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?
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
Questions
Answers
What is direct An equation where as 1 variable increases, the other
variable increases at the same rate.
variation?
The two quantities always have equivalent ratios.
(Like equivalent fractions)
In what 3 ways
can direct
variation be
represented?
Table, equation, and graph
What does direct
variation look
like on a graph?
A straight line through the point of origin
(0,0)
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.
Determine whether the values in the table represent a
direct variation. If so, write a direct variation equation for
the variation. If not, explain.
y
x
y
-1
0
-4
0
1
4
2 2.5
8 10
x
y  4x
Direct-Variation
Equation
Direct Variation
Determine whether the values in the table represent a
direct variation. If so, write a direct variation equation for
the variation. If not, explain.
y
x 3 4 5 6
y 4.5 6 7.5 9
3
y x
2
x
Direct Variation
Direct-Variation
Equation
Determine whether the values in the table represent a
direct variation. If so, write a direct variation equation for
the variation. If not, explain.
y
x
y
1
4
2
6
3
8
4
10
x
The line did not go
through the origin!
NOT
Direct Variation
Determine whether the values in the table represent a
direct variation. If so, write a direct variation equation for
the variation. If not, explain.
y
x
y
-2 -1
4 1
0
0
1
1
x
It is not linear!
NOT
Direct Variation
Finding the values and graphing
using a direct variation equation
At a jumping contest, Evan’s frog jumped 60 inches.
Isabella’s frog jumped 72 inches. Jake’s frog jumped 78
inches. Use the equation y=12x, where y is the number
of inches and x is the number of feet, to find the missing
values in the table.
Evan’s Isabell Jake’s
frog
a’s
frog
frog
Inches
(y)
Feet
(x)
60
72
6
6.5
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 y=60x,
where x is the number of hours and y is the number of
minutes.
Hours (x)
Minutes (y)
0
3
360
24
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 y=9x, 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
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?