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Chapter 13 Graphing Equations 13.1 The Rectangular Coordinate System Ordered pair Coordinate x-axis y-axis Origin Quadrants Graphing an Ordered Pair To graph the point corresponding to a particular ordered pair (x,y), you must start at the origin and move x units to the left or right (right if x is positive, left if x is negative), then move y units up or down (up if y is positive, down if y is negative). Completing Ordered Pair Solutions In general, an ordered pair is a solution of an equation in two variables if replacing the variables by the values of the ordered pair results in a true statement. If you know one coordinate of an ordered pair that is a solution for an equation, you can find the other coordinate through substitution and solving the resulting equation. Find the x and y coordinates of A, B, C, D, E, F. F A E D C B A( , ) B( , ) C( , ) D( , ) E( , ) F( , ) 32 Example: Complete the ordered pair. 1. (3, ___) is a solution of the equation 2 + 5 = −4. 2. (3, ___) is a solution of the equation 3 − = −5. 13.2 Graphing Linear Equations Linear Equation in Two Variables A linear equation in two variables is an equation that can be written in the form Ax + By = C. Where A, B, C are real numbers and A and B not both 0. This form is called standard form. The graph of a linear equation in two variables is a straight line. 1. 2 − = −4 2. = +3 Note: When graphing a linear equation in two variables, if it is • solved for y, it may be easier to find ordered pair solutions by choosing x-values. If it is • solved for x, it may be easier to find ordered pair solutions by choosing y-values. 33