Warm-Up Linear Functions - Edgenuity Inc.
Warm-Up
Linear Functions
Lesson Objectives
By the end of this lesson, you should be able to:
? Determine if a
? Represent a
is linear.
relationship numerically, algebraically, and
graphically.
W
2K
Words to Know
Write the letter of the definition next to the matching word as you work through
the lesson. You may use the glossary to help you.
_____ linear function
A. the point on a graph at which the graph
crosses the ?-axis
_____ point-slope form
B. the slope-intercept form of a linear equation
is given by ? = ?? + ?, where ? is the slope
and b is the ?-intercept
_____ slope-intercept form
C. the point-slope form of a linear equation is
given by ? ? ?1 = ?(? ? ?1 ), where (?1 , ?1 )
is a point on the line and m is the slope
_____ standard form of a
D. a function that can be written in the form
? ? = ?? + ?, where ? and ? are real
numbers; consists of a set of ordered pairs
all lying on the same line
linear equation
_____ ?-intercept
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E. the form ?? + ?? = ?, where ?, ?, and ? are
real numbers such that ? and ? are not both
zero, ? is positive if it is not zero, and the
greatest common factor of ?, ?, and ? is 1
1
Instruction
?
Linear Functions
Lesson
Question
Slide
3
Graphing Functions from Slope-Intercept Form
Graph ? = 2? + 3.
Connect the points to draw the graph.
y
? is the coefficient of ?.
4
? = 2, which we can write as ? =
.
x
?4
?=
4
Remember that the ?-intercept is a point,
so it has coordinates (
,
?4
).
Find the other points by using the slope.
You can go up 2, over to the right 1. You can also go down 2 and 1 to the left.
Standard Form of Linear Equation
Standard form of a linear equation
?? + ?? = ?,
where ?, ?, and ? are real numbers such that ? and ? are not both zero, ? is
if it is not zero, and the greatest common factor of ?, ?, and ?
is
.
Write the equation ?2? + ? = ?3 in standard form.
Multiply the equation through by ?1:
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2? ? ? =
2
Instruction
Linear Functions
Slide
5
Point-Slope Form of Linear Equation
Point-slope form of a linear equation
? ? 5 = 2(? ? 1)
?=2
? ? ?1 = ?(? ? ?1),
where (?1, ?1) is a
on the
Point: (
line and m is the
,
)
.
Write the equation in slope-intercept form.
??5=2 ??1
? ? 5 = 2? ? 2
+ 5
+5
Distribute.
Add 5 to both sides of the equation.
?=
The equations ? ? 5 = 2 ? ? 1 and ? = 2? + 3 are equivalent equations. That
means that if we graphed them, we would get the same exact
10
.
Modeling a Linear Relationship
Movie Tickets
Child: $6
Total Revenue: $1,500
Adult: $9
? = # of child tickets
? = # of adult tickets
6? +
=
You could also change this equation to slope-intercept form to graph it, to look at
the intercepts of the equation.
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3
Instruction
Linear Functions
Slide
12
Modeling a Linear Relationship
Example: Write a linear function to model the following situation:
An airplane is 30,000 ft. in the air and descending 1,000 ft. for each mile it travels.
¡°Descending¡± means it¡¯s going
.
Write the equation.
?=
Or, as a function
?(?) = 30,000 ? 1,000?
The question is: How far away from the airport does the airplane have to start to
descend to land safely? To answer that, we need to find the ?-intercept.
Plug in
for ?.
0 = 30,000 ? 1,000?
1,000? =
?=
The plane needs to start to descend 30
land safely.
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from the airport in order to
4
Summary
?
Linear Functions
Lesson
Question
How do you represent linear relationships?
Answer
Slide
2
Review: Key Concepts
Linear relationships can be written in one of the following forms.
Slope-intercept form: ? = ?? + ?
? is the
, ? is the ?-intercept
form of a linear equation: ?? + ?? = ? ,
? and ? are not both 0, ? is positive if it is not 0, and ?, ?, and ? have no
common factors.
Point-slope form: ? ? ?1 = ?(? ? ?1 )
? is the slope, (?1, , ?1 ) is a
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on the line
5
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