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 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 = -8 2.y = -3x