Transcript Direct 9x

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)
February 16, 2011
1) Write your homework in your agenda:
2) Open your agenda to your behavior card.
3) Open your Homework and Practice
workbook p. 49
4) Here’s your Warm-up….
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
Questions
What is a
function?
How do I find
an equation
for a table of
values?
How do I find
the missing
values in a
table?
Answers
A rule that relates two quantities so that each input
value corresponds to exactly one output value.
1) Compare x and y values to find a
pattern.
2) Write an equation that fits every pair of
values.
Use substitution to solve for the missing value
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
y
3
13
4
16
y is 3 times x + 4.
y = 3x + 4
y = 3(10) + 4
y = 30 + 4 = 34
5
19
6
22
7
25
10
Compare x and y to find a
pattern.
Use the pattern to write an
equation.
Substitute 10 for x.
Use your function rule to find
y when x = 10.
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
y
3
10
4
12
y is 2 times x + 4.
y = 2x + 4
y = 2(10) + 4
y = 20 + 4 = 24
5
14
6
16
7
18
10
Compare x and y to find a
pattern.
Use the pattern to write an
equation.
Substitute 10 for x.
Use your function rule to find
y when x = 10.
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 When 1 quantity always changes by the same factor
as another. The two quantities always have
variation?
equivalent ratios. (Like equivalent fractions)
What does direct
variation look
like on a graph?
In what 3 ways
can direct
variation be
represented?
A straight line through the point of origin
Table, equation, and graph
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
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22
22
22
22
22
22
0
0 1
2
3 4
5 6
7 8
9 10 11 12 13 14
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?