Download 3-5 Equations, Tables, and Graphs - Brown

Tables,
and
Graphs
3-5
Equations, Tables,
and
Graphs
3-5 Equations,
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
33
3-5 Equations, Tables, and Graphs
Warm Up
For each function, find the value
of y for x = 0, x = 4, and x = –5.
1. y = 6x – 3
–3, 21, –33
2. y = 3.8x – 12
–12, 3.2, –31
3. y = 1.6x + 5.9 5.9, 12.3, –2.1
Course 3
3-5 Equations, Tables, and Graphs
Problem of the Day
You buy two fruit baskets. Each basket
contains three bunches of bananas. Each
bunch contains five bananas. How many
bananas do you have?
30
Course 3
3-5 Equations, Tables, and Graphs
Learn to generate different
representations of the same data.
Course 3
3-5 Equations, Tables, and Graphs
Additional Example 1: Using Equations to Generate
Different Representations of Data
The height h of an airplane s seconds from
take-off is h = 12s. Make a table and sketch
a graph of the equation.
Equation
h = 12s
An equation shows how
the variables are related.
Course 3
Helpful Hint
The number of seconds s is
the input value. The depth
d is the output value.
3-5 Equations, Tables, and Graphs
Additional Example 1 Continued
Graph
Table
s
0
1
2
3
h
0
12
24
36
A table identifies
values that make
the function true.
Course 3
50
h
40
30
20
10
0
1
2
3
4
5
s
A graph is a visual image
of the values in the
table.
3-5 Equations, Tables, and Graphs
Check It Out: Example 1
The height h of a helicopter s seconds from
take-off is h = 15s. Make a table and sketch
a graph of the equation.
Equation
h = 15s
An equation shows how
the variables are related.
Course 3
3-5 Equations, Tables, and Graphs
Check It Out: Example 1 Continued
Graph
Table
s
0
h
0
1
2
3
15
30
45
4
60
A table identifies
values that make
the function true.
Course 3
h
75
60
45
30
15
0
1
2
3
4
5
s
A graph is a visual image
of the values in the table.
3-5 Equations, Tables, and Graphs
Additional Example 2: Using Tables to Generate
Different Representations of Data
Use the table to make a graph and to write
an equation.
Course 3
x
0
1
2
y
–1
0
1
3
2
Look for a pattern in the values:
0=1–1
1=2–1
2=3–1
Each value of y is the
value of x minus 1.
3-5 Equations, Tables, and Graphs
Additional Example 2 Continued
Use the table to make a graph and to write
an equation.
y
x
0
1
y
–1
0
2
3
1
2
y=x–1
Course 3
4
2
x
–4 –2
–2
–4
0
2
4
3-5 Equations, Tables, and Graphs
Check It Out: Example 2
Use the table to make a graph and to write
an equation.
Course 3
x
0
1
2
y
3
4
5
3
6
Look for a pattern in the values:
4=1+3
5=2+3
6=3+3
Each value of y is the
value of x plus 3.
3-5 Equations, Tables, and Graphs
Check It Out: Example 2 Continued
Use the table to make a graph and to write
an equation.
x
0
1
2
y
3
4
5
3
6
y=x+3
Course 3
3-5 Equations, Tables, and Graphs
Additional Example 3: Using Graphs to Generate
Different Representations of Data
Use the graph to make a table and to write
an equation.
d
Look for a pattern in the values:
8
4
t
–8 –4
–4
–8
Course 3
0
4
8
4=2
•
1+2
6=2
•
2+2
8=2
•
3+2
3-5 Equations, Tables, and Graphs
Additional Example 3 Continued
Use the graph to make a table and to write
an equation.
Each value of d is 2 times the value of t plus 2.
Course 3
t
0
1
d
2
4
2
3
6
8
d = 2t + 2
3-5 Equations, Tables, and Graphs
Check It Out: Example 3
Use the graph to make a table and to write
an equation.
d
Look for a pattern in the values:
8
4
t
–4 –2
–4
–8
Course 3
0
2
4
2=3
•
1–1
5=3
•
2–1
8=3
•
3–1
3-5 Equations, Tables, and Graphs
Check It Out: Example 3 Continued
Use the graph to make a table and to write
an equation.
Each value of d is
t minus 1.
t
0
1
2
3
Course 3
3 times the value of
d
–1
2
5
8
d = 3t – 1
3-5 Equations, Tables, and Graphs
Lesson Quiz: Part I
1. Make a table and sketch the graph of
w = –2x + 3.
w
Course 3
x
0
1
2
w
3
1
-1
3
-3
4
2
x
–4 –2
–2
–4
0
2
4
3-5 Equations, Tables, and Graphs
Lesson Quiz: Part II
2. Use the table to sketch a graph and write an
equation. y = –x
y
x y
-1 1
0 0
1 -1
2
Course 3
-2
4
2
x
–4 –2
–2
–4
0
2
4
3-5 Equations, Tables, and Graphs
Lesson Quiz: Part III
3. Use the graph to make a table and to write an
equation. y = 4x + 1
x
2
1
0
y
9
5
1
–1 –3
Course 3