Go over homework
3-5
Equations, Tables, and
Graphs
Solution
Any ordered pair that makes an equation true
(2, 6) is a solution of y = 3x
because 6 = 3(2)
An equation can have many solutions
(0, -8) is a solution of y = 3x – 8
Because -8 = 3(0) -8
(-2, 2) is not a solution of y = 3x -8
Because 2 = 3(-2) -8
Linear
Equation
•
•
• lie on a line
if all of its solutions
•
Straight line
Continuous line
Curvy line
An equation that contains two variables can be used as a rule to
generate ordered pairs. When you substitute a value for x, you
generate a value for y. The value substituted for x is called the
input, and the value generated for y is called the output.
Output
Input
y = 10x + 5
In a function, the value of y (the output) is determined by the
value of x (the input). All of the equations in this lesson represent
functions.
Ch. 3-5 Equations, Tables, and Graphs
Example 1: Suppose you wanted to save $3 each week. Make a table and write
an equation to represent your total savings after a given number of weeks. How
much would you save after 15 weeks?
-You need to choose a
variable to represent number
of weeks and total savings.
Then write an equation.
Number of
Weeks (w)
Total
Savings (t)
Equation
t = 3w
0
0
0
1
3
3(1)
2
6
3(2)
3
9
3(3)
The equation t = 3w models your total savings
Use your equation to find out how much money will be saved after 15 weeks by
plugging in 15 for w.
T = 3(15) = $45
Example 2: You buy CD’s from a music store. Each CD costs $15. Make a table
and write an equation to represent the total cost of buying a given number of
CD’s. How much would it cost to buy 12?
-You need to choose a variable to
represent number of CD’s
purchased and cost. Then write an
equation.
The equation C
Number of
CD’s
purchased
(n)
Cost
(c)
Expression
C = 15n
0
0
15(0)
1
15
15(1)
2
30
15(2)
= 15n models your total cost for purchasing n CD’s
Use your equation to find out how much it will cost to purchase 12 CD’s by plugging
in 12 for N.
C = 15(12) = $180
-When you graph linear equations plug in 2 numbers for x and see what you get out
as your y. Then plot the points on a coordinate plane.
Example 3: Graph each linear equation below by picking two values for x and
seeing what you get out as your y. Make a table and then plot your points.
a.) y = 5x – 2
Now plot the points
and draw the line
b.) y = -1/2x + 4
x
y
0
-2
3
1
Now plot the points
and draw the line
x
y
0
4
3.5
1
Example 4: Determine whether each ordered pair below
is a solution to the equation y = 3x – 8
a.) (0,-8)
Y = 3(0) – 8
Y=0–8
Y = -8
Yes
b.) (-2, 2)
Y = 3(-2) -8
Y = -6 – 8
Y= -14
No
c.) (4, 4)
Y = 3(4) -8
Y = 12 – 8
Y= 4
Yes
Example 5: Art Application
An engraver charges a setup fee of $10 plus $2 for every
word engraved. Write a rule for the engraver’s fee. Write
ordered pairs for the engraver’s fee when there are 5, 10,
15, and 20 words engraved.
Let y represent the engraver’s fee and x represent the
number of words engraved.
Engraver’s fee
y
y = 10 + 2x
is
$10
plus
$2
for each
word
=
10
+
2
·
x
Writing Math
The engraver’s fee is determined by the number of words
in the engraving. So the number of words is the input and
the engraver’s fee is the output.
Example 5 Continued
Number of
Words
Engraved
Rule
Charges
Ordered
Pair
x (input)
y = 10 + 2x
y (output)
(x, y)
5
y = 10 + 2(5)
20
(5, 20)
10
y = 10 + 2(10)
30
(10, 30)
15
y = 10 + 2(15)
40
(15, 40)
20
y = 10 + 2(20)
50
(20, 50)
Check It Out! Example 6
What if…? The caricature artist increased his fees. He now
charges a $10 set up fee plus $20 for each person in the
picture. Write a rule for the artist’s new fee. Find the
artist’s fee when there are 1, 2, 3 and 4 people in the picture.
Let y represent the artist’s fee and x represent the number of
people in the picture.
Artist’s fee
y
is
$10
plus
$20
for each
person
=
10
+
20
·
x
y = 10 + 20x
Check It Out! Example 6 Continued
Number of
People in
Picture
Rule
Charges
Ordered
Pair
x (input)
y = 10 + 20x
y (output)
(x, y)
1
y = 10 + 20(1)
30
(1, 30)
2
y = 10 + 20(2)
50
(2, 50)
3
y = 10 + 20(3)
70
(3, 70)
4
y = 10 + 20(4)
90
(4, 90)
When you graph ordered pairs generated by a
function, they may create a pattern.
Example 7A: Generating and Graphing Ordered Pairs
Generate ordered pairs for the function using the given
values for x. Graph the ordered pairs and describe the
pattern.
•
y = 2x + 1; x = –2, –1, 0, 1, 2
Input
x
–2
–1
0
1
2
Output
y
2(–2) + 1 = –3
2(–1) + 1 = –1
2(0) + 1 = 1
2(1) + 1 = 3
2(2) + 1 = 5
•
Ordered
Pair
•
(x, y)
(–2, –3)
(–1, –1)
(0, 1)
(1, 3)
(2, 5)
•
•
The points form a line.
Homework
Pg 132
#5-8 all - make a table and write and
equation
#10-12 all – write down three
coordinates and create the line on graph
paper
Example 7B: Generating and Graphing Ordered Pairs
y = x2 – 3; x = –2, –1, 0, 1, 2
Input
Output
Ordered
Pair
x
y
(x, y)
–2
–1
0
1
2
(–2)2 – 3 = 1
(–1)2 – 3 = –2
(0)2 – 3 = –3
(1)2 – 3 = –2
(2)2 – 3 = 1
The points form a U shape.
(–2, 1)
(–1, –2)
(0, –3)
(1, –2)
(2, 1)
Example 7C: Generating and Graphing Ordered Pairs
y = |x – 2|; x = 0, 1, 2, 3, 4
Input
Output
Ordered
Pair
x
y
(x, y)
0
1
2
3
4
|0 – 2| = 2
|1 – 2| = 1
|2 – 2| = 0
|3 – 2| = 1
|4 – 2| = 2
The points form a V shape.
(0, 2)
(1, 1)
(2, 0)
(3, 1)
(4, 2)
Homework Quiz
1.) A cable company charges $50 to set up a
movie channel and $3.00 per movie
watched. Write a rule for the company’s
fee. Write ordered pairs for the fee when
a person watches 1, 2, 3, or 4 movies.
y = 50 + 3x; (1, 53), (2, 56), (3, 59), (4, 62)