Read the explanation in each lesson carefully, then study the examples given before doing the exercises.

1. Lesson 1.1 Review on Graphing Linear Equations
Linear Equations can be graphed using table of values.
Example 1. Graph x + y = 10
x
3
5
10
y
7
5
y
0
x + y =10
Plot the three points on the coordinate system
and connect .
x
The graph of the linear equation is presented at
the right.
y
Example 2 Graph x - y = 2
x
0
5
2
y
-2
3
0
x-y=2
x

2. Another way to graph linear equations in two variables is by using the slope-intercept
method. Recall that slope is the steepness or inclination of a line. It is the ratio of the vertical
change to the horizontal change, the rise over the run. In the form y = mx + b, m is the slope
and b is the y-intercept. So, it is important that we transform the given equation into the y form
in order to identify the slope and y-intercept. Remember, two points determine a line.
Examples: Transform the equations to y - form. Identify the slope and the y- intercept
1. x + y = 24
y = -x + 24
m = -1, b = 24 2.
-4x -y = 5
y = -4x - 5
m = -4, b = -5
3. -x + 2y = 8
y= 1x+4
2
m= 1, b=4
2

3. Linear equations can be graphed using the slope-intercept form.
Let's graph the equation 3x -2y = 4.
Follow the steps.
•
•
•
•
Transform 3x -2y = 4 to y = mx + b
y = 3 x - 2.
2
The slope (m) of the equation is 3 and the y- intercept (b) is -2.
2
Locate the y-intercept, -2 at the y-axis. Mark the point associated with this.
Starting from the y-intercept move 3 units upward ( rise ) and from this position move 2
units to the right ( run) . Mark this point. ( If the slope is negative move upward then to
the left or move downward then to the right)
•
•
Move again from this point using the ratio of the slope. Mark this point.
Connect the points with a straight line. Use three points
y
Run = 2
x
Rise=3
y-intercept
This is now the graph of 3x - 2y = 4

4. Suppose our equation is -3x -2y = 4
Following the steps the graph now of
-3x -2y = 4 is presented at the right. What have you noticed on the slope?
Did you find any difference between the two equations and their graphs?