MTH 100 CBI
The Rectangular Coordinate System
Objectives
1. Plot Ordered Pairs in the Rectangular
Coordinate System.
2. Determine if an Ordered Pair is a Solution to
an Equation.
3. Find Unknown Coordinates.
4. Graph Equations by Plotting Points.
5. Find x- and y-intercepts.
Objective 1
Objective 2
• A linear equation (in two variables) in
standard form is written as Ax + By = C.
• A solution to a linear equation (in two
variables) is an ordered pair (x, y) that satisfies
the equation (makes it true).
• Example: Determine if (-2, 6) is a solution to
4x + 3y = 10.
Objectives 3 and 4
• The graph of every linear equation is a straight
line (the line may slant upwards, stant
downwards, be horizontal, or be vertical).
• One strategy for graphing a linear equation is to
create a table of values.
• In a table of values, one half of the ordered pair
(either x or y) is given, and the other half is solved
for in the equation.
• Once the ordered pairs have been completed,
their plots should be able to be connected with a
straight line.
Objectives 3 and 4 Example
• Using the equation 4x + 3y = 10, complete the
following ordered pairs and sketch the graph:
1. ( ____, -2)
2. ( 7, ____ )
3. ( ____, 0)
4. ( 0, ____ )
Objective 5
• Now, look back at parts 3 and 4 of the previous
example. Notice that those two points are
located on the x- and y-axis, respectively.
• A point that lies on the x-axis is called the xintercept. To find an x-intercept, set y = 0 and
solve for x.
• A point that lies on the y-axis is called the yintercept. To find a y-intercept, set x = 0 and solve
for y.
Objective 5 Examples
• Find the x-intercept and y-intercept for each
of the following equations:
1. 2x – y = -8
2. y = -3x