6
MODULE
Forms of Linear
Equations
Essential Question: How can you use different
forms of linear equations to solve real-world
problems?
LESSON 6.1
Slope-Intercept Form
LESSON 6.2
Point-Slope Form
LESSON 6.3
Standard Form
LESSON 6.4
Transforming Linear
Functions
LESSON 6.5
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Comparing Properties
of Linear Functions
REAL WORLD VIDEO
Periodic comets have orbital periods of less than 200 years. Halley’s
comet is the only short-period comet that is visible to the naked eye. It
returns every 76 years. You can build functions to represent and model
predictable occurrences, such as the return of Halley’s comet.
MODULE PERFORMANCE TASK PREVIEW
Who Wins the Race
A marathon is a long-distance run that is 26.2 miles long. Marathon events are hosted all
over the world, and participants are a mix of athletes with different skill levels. Most runners
train for many months to prepare for a marathon. How can linear equations be used to
compare the running speeds of two different runners? Stay on track and find out!
Module 6
237
Are YOU Ready?
Complete these exercises to review skills you will need for this module.
Constant Rate of Change
Tell if the rate of change is constant.
Example 1
+1
+1
+1
x
1
2
3
4
y
16
22
28
34
+6
+6
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For a function defined in terms of
x and y, the rate of change of the
function is a ratio that compares the
change in y to the change in x.
+6
6,
The rate of change, _
1
is constant.
change in y
6
rate of change = __ = _
change in x 1
Tell if the rate of change is constant.
1.
x
2
5
8
11
y
6
15
24
33
2.
x
3
6
9
12
y
2
6
11
17
Two-Step Equations
Solve.
Example 2
10 = 3x - 11
10 + 11 = 3x – 11 + 11
21 = 3x
3x
21 = _
_
3
3
7=x
Add 11 to both sides of the equation.
Divide both sides of the equation by 3.
3.
7n + 17 = 59
4.
24 - 4y = 20
5.
34 = 49 – 3b
Linear Functions
Example 3
4 –8
Tell whether y = _
x
represents a linear function.
When a linear equation is written in standard
form, the following are true.
• x and y both have exponents of 1.
4 – 8 does not represent a
y=_
x
linear function because x appears
in the denominator.
• x and y are not multiplied together.
• x and y do not appear in denominators,
exponents, or radicands.
Tell whether the equation represents a linear function.
6.
8x2 + y = 16
Module 6
7.
6x + y = 12
238
8.
3y = 2x + 5
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Solve each equation.