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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