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 to4x + 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 x-intercept. To find an x-intercept, set y = 0 and solve for x.

• A point that lies on the y-axis is called the y-intercept. 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 = -82.y = -3x