Where we’ve been…
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Today, we take our first step into Chapter 3: Linear
Functions – which is fundamentally at the
of Algebra
Before we take our first step, let’s go back and see what
objectives we accomplished in Chapter 2.
In Chapter 2, we…
Solved equations by using the 4 basic operations
Solved one-step, two-step, and multi-step equations
Used formulas to solve real world problems
Now, in Chapter 3, our objective will be to…
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1. Identify linear equations
2. Identify x- and y- intercepts
3. Graph linear equations using the xand y-intercepts or a table of values
with 4 domain values
3.1 Graphing Linear Equations
Our objective:
To identify a linear equation in Standard
Form
To identify the X-intercept and Yintercept of a linear equation
Identifying a Linear Equation
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Ax + By = C
or
Ax – By = C
The exponent of each variable is 1.
The variables are added or subtracted.
A or B can equal zero.
A > 0 (cannot have a negative coefficient)
Besides x and y, other commonly used variables
are m and n, a and b, and r and s.
There are no radicals (sq. root symbols) in the equation.
Every linear equation graphs as a line.
Examples of linear equations
Equation is in Ax + By =C form
2x + 4y =8
6y = 3 – x
Rewrite with both variables
on left side … x + 6y =3
x=1
B =0 … x + 0  y =1
-2a + b = 5
Multiply both sides of the
equation by -1 … 2a – b = -5
4x  y
 7
3
Multiply both sides of the
equation by 3 … 4x –y =-21
Examples of Nonlinear Equations
The following equations are NOT in the
standard form of Ax + By =C:
4x2 + y = 5
x4
xy + x = 5
s/r + r = 3
The exponent is 2
There is a radical in the equation
Variables are multiplied
Variables are divided (can’t have a
variable in the denominator)
x and y -intercepts
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The x-intercept is the point where a line crosses
the x-axis.
The general form of the x-intercept is (x, 0).
The y-coordinate will always be zero.
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The y-intercept is the point where a line crosses
the y-axis.
The general form of the y-intercept is (0, y).
The x-coordinate will always be zero.
Finding the x-intercept
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For the equation 2x + y = 6, we know that
y must equal 0. What must x equal?
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Plug in 0 for y and simplify.
2x + 0 = 6
2x = 6
x=3
So (3, 0) is the x-intercept of the line.
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Finding the y-intercept
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For the equation 2x + y = 6, we know that x
must equal 0. What must y equal?
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Plug in 0 for x and simplify.
2(0) + y = 6
0+y=6
y=6
So (0, 6) is the y-intercept of the line.
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To summarize….
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To find the x-intercept, plug in 0
for y.
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To find the y-intercept, plug in 0
for x.
Find the x and y- intercepts
of x = 4y – 5
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x-intercept:
Plug in y = 0
x = 4y - 5
x = 4(0) - 5
x=0-5
x = -5
(-5, 0) is the
x-intercept
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y-intercept:
Plug in x = 0
x = 4y - 5
0 = 4y - 5
5 = 4y
5
=y
4
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5
(0, 4 )
is the
y-intercept
Find the x and y-intercepts
of g(x) = -3x – 1*
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x-intercept
Plug in y = 0
g(x) = -3x - 1
0 = -3x - 1
1 = -3x
1

=x
3
1
(  3 , 0) is the
x-intercept
*g(x) is the same as y
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y-intercept
Plug in x = 0
g(x) = -3(0) - 1
g(x) = 0 - 1
g(x) = -1
(0, -1) is the
y-intercept
Find the x and y-intercepts of
6x - 3y =-18
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x-intercept
Plug in y = 0
6x - 3y = -18
6x -3(0) = -18
6x - 0 = -18
6x = -18
x = -3
(-3, 0) is the
x-intercept
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y-intercept
Plug in x = 0
6x -3y = -18
6(0) -3y = -18
0 - 3y = -18
-3y = -18
y=6
(0, 6) is the
y-intercept
Find the x and y-intercepts
of x = 3
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x-intercept
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Plug in y = 0.
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(3, 0) is the x-intercept.
y-intercept
vertical line never
There is no y. Why? crosses the y-axis.
● There is no y-intercept.
● x = 3 is a vertical line
so x always equals 3.
x
Find the x and y-intercepts
of y = -2
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x-intercept
Plug in y = 0.
y cannot = 0 because
y = -2.
● y = -2 is a horizontal
line so it never crosses
the x-axis.
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y-intercept
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y = -2 is a horizontal line
so y always equals -2.
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(0,-2) is the y-intercept.
x
is no x-intercept.
y