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By Edward Kohn, David Alan Herzog

By way of pinpointing the things you really want to understand, not anyone does it higher than CliffsNotes. This quickly, powerful educational is helping you grasp center algebraic techniques -- from linear equations, kinfolk and features, and rational expressions to radicals, quadratic platforms, and factoring polynomials -- and get the very best grade.
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Solve this equation for y. Ax + By = C By = –Ax + C y = - BA x + CB The value - AB becomes the slope of the line, and CB becomes the y-intercept value. If - AB is replaced with m and CB is replaced with b, the equation becomes y = mx + b. This is known as the slope-intercept form of a nonvertical line. Example 11: Find the slope and y-intercept value of the line with the equation 3x – 4y = 20. Solve for y. 3x – 4y = 20 –4y = –3x + 20 y = 34 x – 5 Therefore, the slope of the line is 34 , and the y-intercept value is –5.

This means that the “(0, 0) side” of the boundary line is the desired region to be shaded. Now, shade that region as shown in Figure 2-12. F 4/19/01 8:50 AM Page 37 Chapter 2: Segments, Lines, and Inequalities 37 Figure 2-12 The shading is below the line. 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 ≥.

Example 4: A line passes through (–5,8) with a slope of 23 . If another point on this line has coordinates (x,12), find x. y 2 - y1 m = x 2 - x1 2 = 12 - 8 3 x - ^ - 5h 2= 4 3 x+5 2 ^ x + 5h = 4 ^ 3 h 2x + 10 = 12 2x = 2 x=1 Slope of Parallel and Perpendicular Lines Parallel lines have equal slopes. Conversely, if two different lines have equal slopes, they are parallel. F 4/19/01 8:50 AM Page 29 Chapter 2: Segments, Lines, and Inequalities 29 their slopes are negative reciprocals (actually, opposite reciprocals) of one another, or the product of their slopes is –1.

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