Math 95
Section 3.2 Notes
Linear Equations in Two Variables
Objectives:
Students will be able to:
 Graph linear equations in 2 variables by plotting points
 Determine x and y intercepts
 Graph horizontal and vertical lines
Linear Equation in 2 Variables
Standard Form for a Line
Ax + By = C
Where A, B, and C are integers.
Example:
Determine whether the given point is a solution to the equation.
a.
y
5
x2
2
4

 , 3 
5

5  4 
 2
2 5
3  2  2
3 
3  0 False statement
b.
1
x3
3
1
4   3   3
3
4  1 3
y
 3, 4 
4  4 True statement
Example:
Complete the table and graph the corresponding ordered pairs. Draw the line defined by
the points.
a.
x y 3
X
2
0
-1
3
Y
1
3
4
0
To find the first point, you will plug in 2 for x and solve for y.
To find the second point, you will plug in 3 for y and solve for x.
To find the third point, you will plug in -1 for x and solve for y.
To find the third point, you will plug in 0 for y and solve for x.
So you will plot the points first. Once you have to points plotted, you will draw a line
through all the points. You should see that you should have a straight line.
b.
y  3x  3
X
-2
-1
0
Y
3
0
-3
To find the first point, you will plug in -2 for x and solve for y.
To find the second point, you will plug in 0 for y and solve for x.
To find the third point, you will plug in 0 for x and solve for y.
So you will plot the points first. Once you have to points plotted, you will draw a line
through all the points. You should see that you should have a straight line.
c.
y  2
X
0
-3
5
Y
-2
-2
-2
Since your equation is y = -2, it does not matter what value x takes on. The y-value will
always be -2.
So you will plot the points first. Once you have to points plotted, you will draw a line
through all the points. You should see that you should have a straight line.
Example:
Find the x and y intercepts and then graph.
a.
x y 4
y-intercept: (0, 4) Plug in 0 for x and solve for y.
x-intercept: (4, 0) Plug in 0 for y and solve for x.
b.
2
x 1
3
y-intercept: (0, -1) Plug in 0 for x and solve for y.
x-intercept: (3/2, 0) Plug in 0 for y and solve for x.
y
c.
x  2y
y-intercept: (0, 0) Plug in 0 for x and solve for y.
x-intercept: (0, 0) Plug in 0 for y and solve for x.
Since the x and y intercept are the same, we need another point to graph the line. So let
y = 1, then x = 2.