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Additional info for Algebra II (Cliffs Quick Review)
Y 4 3 3x + 4y <12 2 1 −3 −2 −1 1 2 3 x 3x + 4y = 12 4 −1 −2 −3 Example 14: Graph y ≥ 2x + 3. First, graph y = 2x + 3 (see Figure 2-13). Figure 2-13 This boundary is solid. y 5 (1,5) 4 3 (0,3) 2 (−1,1) −3 −2 −1 1 1 2 3 x −1 −2 y = 2x + 3 −3 Notice that the boundary is a solid line, because the original inequality is ≥. Now, select a point not on the boundary, say (2, 1), and substitute its x and y values into y ≥ 2x + 3. F 38 4/19/01 8:50 AM Page 38 CliffsQuickReview Algebra II y ≥ 2x + 3 ? 1 $ 2(2) + 3 ?
Select a point not on the boundary line and substitute its x and y values into the original inequality. 3. Shade the appropriate area. If the resulting sentence is true, then shade the region where that test point is located, indicating that all the points on that side of the boundary line will make the original sentence true. If the resulting sentence is false, then shade the region on the side of the boundary line opposite to where the test point is located. F 36 4/19/01 8:50 AM Page 36 CliffsQuickReview Algebra II Example 13: Graph 3x + 4y < 12.
A horizontal line that is not the x-axis will have no x-intercept. 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.
Algebra II (Cliffs Quick Review) by Edward Kohn, David Alan Herzog