Algebra 1 Notes A.7 Graphing Linear Equations
Mr. Hannam
Name: ___________________________________________ Date: _____________ Block: _______
Graphing Linear Equations

Linear equations graph lines

The standard form of a linear equation is: Ax + By = C

Example of an equation in two variables: 2x + 5y = 8

Solutions are ordered pairs that make the equation true

(-1, 2) is a solution to the above equation

How can we prove this?_______________________________________

How many different solutions are there to the equation?___________________
Example: Is (3, 4) a solution to 3x – y = 7? Is (1, -4) a solution?
Substitute the values of the ordered pairs back into the original equation:
Test (3, 4): 3(3) – 4 =? 7
Test (1, -4): 3(1) –(-4) =? 7
9 – 4 =? 7
3 + 4 =? 7
5 =? 7
X (3, 4) is not a
3 + 4 =? 7
solution
solution!
 Are there other solutions to this equation?
(1, -4) is a

Try the following ordered pairs: (2, -1), (3, 2), (4, 5)

How many solutions do you think there are to the equation? The graph holds the
answer…
Graphing Linear Equations Using a Table of Values

Graph of an equation in two variables using a table of values

The graph is the set of points in a coordinate plane that represent all solutions to the
equation. The domain is all real numbers: {x | x}

Make a table of values, plot some points to recognize a pattern, connect the points.

Choose convenient (easy!) values from the domain when building the table.
Example: Graph the equation y = 2x + 3
Step 1: Make a table of values:
Step 2: Plot the points:
Step 3: Connect the points:
x
-2
-1
0
1
2
y
Algebra 1 Notes A.7 Graphing Linear Equations
Mr. Hannam Page 2
Examples: Graph the following linear equations…
1) y = -3x + 1
x

2) Graph y = 3
y
x
3) Graph x = -2
y
x
y
Which of the above graphs are functions? Explain ____________________________________
Limiting Domain
 Sometimes we limit the value of the domain.

For example, if the domain represents time, we would not want to have any negative
values. Limiting the domain will limit the range.
Examples: Graph the functions using the limited domain. Identify the range.
a) y = -4x – 3 with domain x ≤ 0
range__________
b) y = -
1
x + 1 with domain x  1
2
range ____________