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Additional info for Algebra II (Cliffs Quick Review)
Y 4 (0,4) 3 2 1 −3 −2 −1 −1 (6,0) 1 2 3 4 5 x 6 2x+3y =12 −2 −3 Notice that Figures 2-6 and 2-7 are exactly the same. Both are the graph of the line 2x + 3y = 12. Example 8: Draw the graph of x = 2. As shown in Figure 2-8, x = 2 is a vertical line whose x-coordinate is always 2. Figure 2-8 x = 2 for all y values. y 3 x=2 2 1 −3 −2 −1 1 2 3 x −1 −2 −3 Example 9: Draw the graph of y = –1. As shown in Figure 2-9, y = –1 is a horizontal line whose y-coordinate is always –1. F 4/19/01 8:50 AM Page 33 Chapter 2: Segments, Lines, and Inequalities Figure 2-9 33 y = –1 for all x values.
If you use the x-intercept and y-intercept method, you get x-intercept (4, 0) and y-intercept (0, 3). If you use the slope-intercept method, the equation, when written in y = mx + b form becomes y= - 34 x + 3 Because the original inequality is <, the boundary line will be a dashed line. Look at Figure 2-11. Figure 2-11 The boundary is dashed. y 4 3 2 1 −3 −2 −1 1 2 3 −1 x 4 3x + 4y = 12 −2 −3 Now, select a point not on the boundary, say (0, 0). Substitute this into the original inequality: 3x + 4y < 12 ?
F 30 4/19/01 8:50 AM Page 30 CliffsQuickReview Algebra II ■ y-intercept. The y-intercept of a graph is the point at which the graph will intersect the y-axis. It will always have an x-coordinate of zero. A vertical line that is not the y-axis will have no y-intercept. One way to graph a linear equation is to find solutions by giving a value to one variable and solving the resulting equation for the other variable. A minimum of two points is necessary to graph a linear equation. Example 6: Draw the graph of 2x + 3y = 12 by finding two random points.
Algebra II (Cliffs Quick Review) by Edward Kohn, David Alan Herzog