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Algebra I
SOL A.6 (Sec. 4.2)
Name:
Block:
Date:
Graphing Linear Equations using a Table
Essential Quet
Essential Question(s): How many solutions are there to a linear equation? How do you use the
graphing calculator to fill in the x-y table? How do you graph a function with a restricted domain?


So far, we have been solving equations with one variable.
Now, we will be working with equations with two variables (x and y) like 2x + 5y = 8.
Solutions of Equations in Two Variables
The solution of an equation in two variables is an _______________ ____________
that produces a TRUE statement when the values of x and y are substituted
into the equation.
Example: Which ordered pair is a solution of 3x – y = 7?
A) (3, 4)
B) (1, -4)
C) (5, -3)
D) (-1, -2)
Practice: Tell whether the ordered pair is a solution of the equation.
1)
3x – 2y = 5; (1, -1)
2) -7x – 4y = -1 ; (-3, -5)
3) y = -7 ; (-7, 0)
Every ordered pair that makes the equation true is a solution to the equation.
If you graph the equation, every ordered pair on the graphed line will be a solution
to the equation.
Graphing an Equation
1. Write the equation in slope- intercept form (“y=” form).
2. Make an input-output table:
 Choose a few values for “x” (-1, 0 and 1 work well much of the time) and
find the values of y.

You can choose any values you want; it’s helpful to include negative values
and zero.

Just make sure your graph is big enough!
3. Graph the ordered pairs.
If they do not form a line, go back and check your work.
4. Connect the points to form a straight line.
(use arrows to indicate the graph goes on forever in both directions)
Example 1: Graph the following equation: 2x – 4y = 12
x
y
( x, y )
Practice: Graph the following equation: 10y = 20x – 30
x
y
( x, y )
Example: Graph the following equation:
2y + x = 4
Use the calculator to help you fill the table.



Choose
button
Enter the equation into Y1
Put fractions in parentheses when entering them into the calculator.

Use

To see the
X
to get the “x” variable.
, enter
Y
,
.
Practice: Graph the equation:
Use the calculator to help you fill the table.
X
y + 3x = -2
Y
Special Cases
Type
Equation
(Picture)
Horizontal
Vertical
Practice graphing special cases:
1) y = 3
x
y
Crosses
Passes through the
point
2) x = 1
x
y
3) y = -2
x
y
4) x = 4
x
y
Is a horizontal line a function? ________
Is a vertical line a function? _______
Graphing Linear Functions
Any equation in the form Ax + By = C is a function, provided B ≠ 0.
(When B = 0, the linear equation is a
,
which is ________ a function.
If the domain of a linear function is not specified, it is understood to be all real numbers.
This means the range is all real numbers also.
(The graph will be a line with arrows on both ends).
Graphing Linear Functions with restricted domains:
1)
2)
3)
4)
5)
Write equation in function form (“y =”).
Make a table.
Plot the ordered pairs.
Connect the points with a ray or line segment, depending on the domain.
Identify the range.
Example 1: Graph the function y = -3x + 1 with the Domain = { x ϵ  | -1 ≤ x ≤ 2 }
x
y
Range:
Example 2: Graph the function y = 2x – 4 with the Domain = { x ϵ  | x ≥ 0 }
x
y
Range:
Summary: