3.1 Solving Equations Using Addition and Subtraction

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3-3B Linear FunctionsGraphing using Intercepts
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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An x-intercept is the x-coordinate of a point
where a graph crosses the x-axis.
A y-intercept is the y-coordinate of a point
where a graph crosses the y-axis.
y










coordinate (0,4) y-intercept is 4

x
coordinate is (3,0) x-intercept is 3

The x-intercept and the y-intercept are numerical
values. They are NOT ordered pairs!
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Example 1 Use the graph to find the x-intercept
of the line.
y
1. Locate the x-intercept.










2. Identify the coordinate.

x
(2,0)
2
3. Name the x-intercept.
The x-intercept is a numerical value. It is NOT
an ordered pair!
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Example 2 Use the graph to find the y-intercept
of the line.
y
1. Locate the y-intercept.










x
2. Identify the coordinate.
(0,3)
3

3. Name the y-intercept.
The y-intercept is a numerical value. It is NOT
an ordered pair!
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Example 3 Use the graph to find the x-intercept
and the y-intercept of the line.
y










Name the x-intercept.
x-intercept is 4

x
Name the y-intercept.
y-intercept is 4

Do not write x 4 or y -4. The answers are
NOT equations.
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Can you use the graph to find the x-intercept and
the y-intercept of the line?
y
Not all intercepts are integers.
i









Some of your homework problems will give you the
equation of the line and not the graph. Given an
equation, you can find the intercepts.
x
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Find the x-intercept of the graph of equation 8x
5y 2.
Write equation.
Substitute zero for y because at the x-intercept
the y-coordinate is zero.
Solve for x.
Name the intercept.
When finding the x-intercept, solve the equation
for x. The answer is a numerical value not an
equation!
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Find the y-intercept of the graph of equation 3x
6y 18.
Write equation.
Substitute zero for x because at the y-intercept
the x-coordinate is zero.
Solve for y.
Name the intercept.
When finding the y-intercept, solve the equation
for y. The answer is a numerical value NOT an
equation!
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Example 4 Find the x-intercept and the
y-intercept of the graph of equation 5x 2y 20
Write equation.
Write equation.
Find the y-intercept. (Solve the equation for
y.)
Find the x-intercept. (Solve the equation for
x.)
Name the y-intercept.
Name the x-intercept.
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Example 5 Find the x-intercept and the
y-intercept of the graph of equation 3x 4y 12
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In the previous lesson you learned to graph an
equation using a table of values.
In this lesson you will learn how to make a quick
graph using the intercepts. The Quick Graph
process works because only two points are needed
to determine a line.












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In the previous lesson you learned to graph an
equation using a table of values.
In this lesson you will learn how to make a quick
graph using the intercepts. The Quick Graph
process works because only two points are needed
to determine a line.












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In the previous lesson you learned to graph an
equation using a table of values.
In this lesson you will learn how to make a quick
graph using the intercepts. The Quick Graph
process works because only two points are needed
to determine a line.












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Making a Quick Graph
1. Find the intercepts.
2. Draw a coordinate plane that includes the
intercepts.
3. Plot the intercepts and draw a line through
them.
How many solutions are there to an equation in x
and y?
infinitely many solutions
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Graph the equation 2x 5y 10 using intercepts.
Write equation.












Find the x-intercept

x

Write equation.
Find the y-intercept
y
Draw a coordinate plane that includes (5,0) and
(0,2).
Plot the coordinates for the x-intercept and
y-intercept.
Draw a line through the points.
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Graph each equation using intercepts.
Example 6 3x 4y 12
Example 7 3x 2y 12
Example 8 y 4x 40
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Example 6 Graph 3x 4y 12 using intercepts.













x

y
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Example 7 Graph 3x 2y 12 using intercepts.














x
y
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Example 8 Graph y 4x 40 using intercepts.













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x
20
20
20
y
Find an appropriate scale that includes points
(10,0) and (0,40). Use the same scale on both
axis.
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Will all equations have an x-intercept and a
y-intercept?
Vertical lines will only have an x-intercept.
Horizontal lines will only have a y-intercept.
You can graph a line using one point, if you know
it is a vertical or horizontal line! How can you
tell by looking at the equation?
Horizontal and vertical lines have only one
variable in the equation!
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Remember standard form for a linear equation
y
Graph x -3










This is why you could not write the x-intercept
as an equation x-3.

x
When B is equal to zero you will have an
equation with one variable.
x -3 is the graph of a vertical line.
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Graph y -3










When A is equal to zero you will have an
equation with one variable.
x

y
y -3 is the graph of a horizontal line.
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Example 9 Graph x 4.
Example 10 Graph x 2.
Example 11 Graph y 4.
Example 12 Graph y 2.
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Example 9 Graph x 4.
Example 10 Graph x 2.






















x
x
y
y
How did you know by looking at the equation that
it would NOT graph as a diagonal line?
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Example 11 Graph y 4.
Example 12 Graph y 2.





















x
x

y
y
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Homework
Pg.159-161 18-2330-3236-3745,49,50,55,61,63.
Algebra rocks!