13.1 Graphing Linear Equation (Using a Table of Values)
Terms to Know—Defined
Example
Ordered pair:
Linear equation:
How can you tell…
 From an table

From a graph

From an equation
Solution (points)
Input values—(x) are the values you put “into”
the expression
*domain
Output values—(y) are the values you get “out”
when you evaluate the expression
*range
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x- and y-axis
Tables can be horizontal
Tables can be vertical--easier to see the solution points (x, y)
(x, y)
Input
Equation
Output
The points you
(x)
(y)
plot—solution points
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Graph an Equation
1. Make a table of values—choose input (x) values to solve for output (y)
values solution points (always choose 0 and at least one negative
and one positive value)
2. Plot the solution points
3. Draw a line through the points—label the line with the equation
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Graphing a horizontal and vertical line
Key Idea

The graph of y = b is a horizontal
line passing through (0, b)—“y lies
down.”

The graph of x = a is a vertical line
passing through (a, 0)—“x is stuck
standing up.”
Advantages and Disadvantages of Tables, Graphs, and Equations
Example
Advantage & Disadvantage
Words
You have $30 in your lunch
account and plan to spend $2.00
each school day.
a. Write and graph a linear
equation that represents the
balance in your lunch account.
b. How many school days will it
take to spend all of the money in
your lunch account?
Equation
y = –2x + 30
x
–10
–5
0
5
10
15
Table
y
50
40
30
20
10
0
3
Graph
Sometimes you will be asked to “solve for y”—that simply means, solve
the equation so that you get y= (this is called writing it in “slopeintercept” or y= form)
e.g.: y – 3x = 1
e.g.: 5x + 2y = 4
e.g.: - 1 y + 4x = 3
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13.2 Slope of a Line (Review)
Terms to know:
Slope:
Table:
Graph:
5
rise = y - change = y 2 - y 1
run x - change x 2 - x 1
Slope Formula: y 2 - y 1 = slope (m)
x 2 - x1
Sometimes you may be asked to find a missing coordinate given the slope
and most of the coordinates.
e.g. (–4, y), (6, –7); m =
-
1
5
*The slope between any pairs of points on the same line will be the same!
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13.2 Extension—Slopes of Parallel and Perpendicular Lines
Parallel Lines: Lines in the same plane (flat surface) that do not (ever)
intersect
What’s True about Parallel Lines
Perpendicular Lines: Lines in the same plane (flat surface) that intersect
at right angles (90°)
What’s True about Perpendicular Lines
How can you use determine whether lines are parallel or perpendicular?
Look at the slopes of the lines! You can’t just “eye-ball” it!
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13.4 Graphing Linear Equations in Slope-Intercept Form
y = mx + b is the slope-intercept form of a linear equation
*The equation (when in y= or slope-intercept form) gives you the
y-intercept (0, b) and the slope of the line—it’s right there!
Notes:
Intercepts—will be more useful when discussing “standard form” of a
linear equation
x-intercept—(a, 0)
y-intercept—(0, b)
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Graphing a linear equation in slope-intercept form—you don’t need a table
1. Identify the slope and y-intercept (m = _____; b = _____)
2. Plot the y-intercept on the graph.
3. Use the slope æ rise ö to plot several other points (in both directions)—be
ç
÷
è run ø
careful of the sign of the slope—it will tell you the direction of your
line
4. Connect through the plotted points with arrows on the ends; label the
line with the equation
5. All of the points on that line (created by connecting the plotted points)
are solution points to the equation—you can now use the line to make
predictions about values not plotted
*A proportional relationship is one that goes through the origin; the ratio
of y is constant; y = k and the line travels through the origin
x
x
13.5 Graphing Linear Equations in Standard From (ax + by = c)
Standard form is often used what two variables are being described—e.g.
(# math books, # science books) and deals with “first quadrant” data
I carry 24 pounds of textbooks from my room to Mrs. Miller’s room.
Each math book (x) weighs 2 pounds and each science book (y) weighs 3
pounds.
2x + 3y = 24

Using a Table and Standard Form—choose x-values and solve for y or
choose y-values and solve for x
Notes:
# of math books (x)
# of science books (y)
0
8
1
22 *
3
4
16 *
3
6
4
12
0
Intercepts: (0, 8) and (12, 0)—what do they mean with respect to what I
carry?
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
Using Intercepts—eliminate the rest of the table and use only the
“mini” intercept table:
x
y
0
b
a
0
*Remember, you can make a line with only two points!
*Remember to label the x- and y-axis
Ticket Sales: You sold $16.00 worth of tickets. Write an equation to
identify the different combinations of tickets you might have sold.
1. Identify the variables.
2. Write the equation:
3. Use the intercepts—plot them then connect through them
4. Label the line with the equation.
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Say Cheese: You sold $16.00 worth of cheese. Write an equation to
identify the different combinations of cheese (lbs.) you might have
sold.
1.
2.
3.
4.
Identify the variables.
Write the equation:
Use the intercepts—plot them then connect through them
Label the line with the equation.
*Although the line identifies all possible solutions to the equation,
some of those values “don’t make sense.” Why?
*Some students may choose to rewrite an equation in slope-intercept
form and graph it from there.
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13.6 Writing Equations in Slope-Intercept Form
Notes:
Given a Graph:
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Given Two Points:
5. (3, 8), (–2, 8)
6. (4, 3), (6, –3)
7. (–1, 2), (8, –1)
13.7 Writing Equations in Point-Slope Form—you only need a point on
the line and the slope of the line
*I call this a “path-way” form of a linear equation—it is used to get to
slope-intercept form
*You can graph an equation using a point and the slope
Can use the slope formula in a different way:
m = y 2 - y1 
y - y 1 = m x - x1 where x1 and y1 are the x- and yx 2 - x1
values that you know or are given.
(
)
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Given the slope and a point
Given two points
Given a written description—real-world
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