Warm Up

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Preview
Warm Up
California Standards
Lesson Presentation
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Warm Up Evaluate each expression for the given
value of the variable. 1. 4x 1 for x 2 2.
7y 3 for y 5 3. x 2 for x 6 4. 8y
3 for y 2
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19
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Most movies shown in theaters are shot using
film. The table shows the relationship between
the duration of a movie in minutes and the length
of the film in feet. Look for a pattern in the
table.
Duration of a Movie (min) Length of Film Needed (ft)
1 90
2 180
3 270
90(1) 90
90(2) 180
90(3) 270
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The length of the film in feet is 90 times the
duration of a movie in minutes. An equation in
two variables can represent this relationship.
Length in feet
is
90
times
duration in minutes.
90
x
y

.
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Additional Example 1 Writing Equations from
Tables
Write an equation in two variables that gives the
values in the table. Use your equation to find
the value of y for the indicated value of x.
x 3 4 5 6 7 10
y 12 16 20 24 28
y is 4 times x.
y 4x
y 4(10)
y 40
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Check It Out! Example 1
Write an equation in two variables 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 5 6 7 8 9
y is 2 more than x
y x 2
y 10 2
y 12
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You can write equations in two variables for
relationships that are described in words.
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Additional Example 2 Translating Words into Math
Write an equation for the relationship. Tell what
each variable you use represents.
The height of a painting is 7 times its width.
h height of painting
w width of painting
h 7w
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Check It Out! Example 2
Write an equation for the relationship. Tell what
each variable you use represents.
The height of a mirror is 4 times its width.
h height of mirror
w width of mirror
h 4w
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Additional Example 3 Problem Solving Application
The school choir tracked the number of tickets
sold and the total amount of money received. They
sold each ticket for the same price. They
received 80 for 20 tickets, 88 for 22 tickets,
and 108 for 27 tickets. Write an equation for
the relationship.
The answer will be an equation that describes the
relationship between the number of tickets sold
and the money received.
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You can make a table to display the data.
Let t be the number of tickets. Let m be the
amount of money received.
t 20 22 27
m 80 88 108
m is equal to 4 times t.
m 4t
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Substitute the t and m values in the table to
check that they are solutions of the equation m
4t.
m 4t (20, 80)
m 4t (22, 88)
m 4t (27, 108)
?
?
?
80 4 20
88 4 22
108 4 27
?
?
?
80 80
88 88
108 108
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Check It Out! Example 3
The school theater tracked the number of tickets
sold and the total amount of money received. They
sold each ticket for the same price. They
received 45 for 15 tickets, 63 for 21 tickets,
and 90 for 30 tickets. Write an equation for the
function.
The answer will be an equation that describes the
relationship between the number of tickets sold
and the money received.
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You can make a table to display the data.
Let t be the number of tickets. Let m be the
amount of money received.
t 15 21 30
m 45 63 90
m is equal to 3 times t.
m 3t
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Substitute the t and m values in the table to
check that they are solutions of the equation m
3t.
m 3t (15, 45)
m 3t (21, 63)
m 3t (30, 90)
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45 3 15
63 3 21
90 3 30
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45 45
63 63
90 90
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Lesson Quiz
1. Write an equation in two variables that gives
the values in the table below. Use your equation
to find the value for y for the indicated value
of x. 2. Write an equation for the
relationship. Tell what each variable you use
represents. The height of a round can is 2 times
its radius.
x 0 1 3 5 7
y 0 3 9 15
y 3x 21
h 2r, where h is the height and r is the radius