3.2 Graphing Linear Equations
Linear Equation in Two Variables
Ax + By = C
(Standard Form)
A, B, and C are integers
A and B can’t both be 0
Solutions to Equations w/ Two
Variables
Ex. Is (3, -2) a solution to 2x – y = 8?
(3, -2)
(x, y)
2x – y = 8
2(3) – (-2) = 8
6 + 2 =8
8 =8
Since (3, -2) satisfies the equation (makes a
TRUE stmt), YES, (3, -2) is a solution.
Ex. Determine if the ordered pairs are
solutions to the equation.
y = 8 – 4x (8, 1), (2, 0), (3, -4)
(8, 1)
(x, y)
y = 8 – 4x
1 = 8 – 4(8)
1 = 8 – 32
1 = -24
False, so NO, (8, 1) is not a solution.
y = 8 – 4x (8, 1), (2, 0), (3, -4)
(2, 0)
(x, y)
y = 8 – 4x
0 = 8 – 4(2)
0=8–8
0=0
True, so YES, (2, 0) is a solution.
y = 8 – 4x (8, 1), (2, 0), (3, -4)
(3, -4)
(x, y)
y = 8 – 4x
-4 = 8 – 4(3)
-4 = 8 – 12
-4 = -4
True, so YES, (3, -4) is a solution.
Complete Ordered Pair Solutions of
Equations
x
Ex. Complete the table of
solution for 2x – 5y = 10
x = 10
2x – 5y = 10
2(10) – 5y = 10
20 – 5y = 10
20 – 5y – 20 = 10 – 20
-5y = -10
-5y = -10
-5 -5
y=2
y=0
2x – 5y = 10
2x – 5(0) = 10
2x – 0 = 10
2x = 10
2x = 10
2
2
x=5
y
(x, y)
10 2
(-2, 5)
5
(-1, -2)
0
Graphing Lines
1) Find at least 3 ordered pairs that satisfy the
equation. (Create a table of solutions.)
2) Plot the 3 ordered pairs as points.
3) Draw a line through the points.
NOTE:
 solns. to an eqn. are points on its line
 points on a line are solns. to the eqn.
Graphing Equations
Ex. Graph the equation: y = 3x + 1
x = -1
y = 3(-1) + 1
y = -3 + 1
y = -2
x=0
y = 3(0) + 1
y=0+1
y=1
x=1
y = 3(1) + 1
y=3+1
y=4
x
y
(x, y)
-1
-2
(-1, -2)
0
1
(0, 1)
1
4
(1, 4)
Ex. Graph y = 3x + 1
y
(1, 4)
x
y
-1
-2
0
1
1
4
3
2
(0, 1)
1
x
-3
-2
-1
1
-1
(-1, -2)
-2
-3
2
3
Ex. Graph y = -4x
y
x = -1
y = -4x
y = -4(-1)
y=4
(-1, 4)
3
2
1
(0, 0)
x
-3
-2
-1
1
-1
-2
2
3
x=0
y = -4(0)
y=0
-3
(1, -4)
x=1
y = -4(1)
y = -4
x
y
-1
4
0
0
1
-4
Graphing by Solving for y first
Ex. Graph x – 3y = -3 by solving for y first.
x – 3y = -3
x – 3y – x = -3 – x
-3y = -x – 3
-3y = -x – 3
-3 -3 -3
y=⅓x+1
When you create
your table of values,
pick multiples of 3
for x!
Ex. Graph the line y = ⅓x + 1
x = -3
y = ⅓x + 1
y = ⅓(-3) + 1
y = -1 + 1
y=0
y
3
(3, 2)
2
1
(0, 1)
x
-3
(-3, 0)
-2
-1
1
-1
2
3
x=0
y = ⅓x + 1
y = ⅓(0) + 1
y=0+1
y=1
-2
-3
x=1
y = ⅓x + 1
y = ⅓(1) + 1
y=1+1
y=2
x
X
y
-3
0
0
1
3
2
Show how to graph in WebAssign
Groups
Pages 203 – 205: 10, 19, 40, 53, 61, 64