Graphing Linear Equations Section 3.2 Graphing Linear Equations

The Rectangular Coordinate System A rectangular coordinate system consists of a horizontal number line and a vertical number line. x y 1 2 3 4 1 2 3 4 An ordered pair (x, y) represents a point on the coordinate system. y-axis x-axis The ordered pair (3, 4) means that x = 3 and y = 4. (3, 4)

Linear Equations The graph of any linear equation in two variables is a straight line. To Graph a Linear Equation Find three ordered pairs that are solutions to the equation. Plot the points. Draw a line through the points.

Example Graph the equation y = –x + 3 by plotting points. Choose any value for x and find the corresponding y-value. For x = 1, y = –(1) + 3 = 2. (1, 2) is one of the solutions. Find three ordered pairs (solutions) to graph the line. x y 1 2 3 4 1 2 3 4 (1, 4) (1, 2) (2, 1) x y 1 2 1 4

Graphing by Plotting Intercepts The x-intercept of a line is the point where the line crosses the x-axis; it has the form (a, 0). The y-intercept of a line is the point where the line crosses the y-axis; it has the form (0, b).

Intercept Method of Graphing Find the x-intercept by letting y = 0 and solving for x. Find the y-intercept by letting x = 0 and solving for y. Find one additional ordered pair so that we have three points with which to plot the line.

Example Graph the equation –3y – 2x = – 6 by using the x- and y-intercepts. Let x = 0 –3y – 2(0) = – 6 y = 2 y-intercept = (0, 2) Let y = 0 –3(0) – 2x = –6 x = 3 x-intercept = (3, 0) x y 1 2 3 4 1 2 3 4 y-intercept (3, 4) (0, 2) (3, 0) x-intercept

Horizontal Lines The graph of the equation y = b, where b is any real number, is a horizontal line through the point (0, b).

Example Graph. a. y = 2 b. y = –3 (0, 2) (0, 3) 1 2 3 4 1 2 3 4

Vertical Lines The graph of the equation x = a, where a is any real number, is a vertical line through the point (a, 0).

Example Graph. a. x = –4 b. x = 2 (4, 0) (2, 0) 1 2 3 4 1 2 3 4 y 1 2 3 4 1 2 3 4 x y 1 2 3 4 1 2 3 4 (4, 0) (2, 0)

Example Graph 2x + 1 = 11 Solve the equation for x. 2x + 1 = 11 2x = 10 x = 5