y = mx + b stope The slope goes down 2 and right 3: rise -2 run y = 2 3 x +4 The y-intercept is 4. 1 0 2 Linear inequalities in two variables, such as y > 2x - 4, are graphed by first drawing either a dashed line (for < or >) or a solid line (for ≤ or 2). Then the region above or below that line is shaded to show which points satisfy the inequality. Chapter 1 also introduced transformations. In Chapter 2, you will further investigate transformations of linear functions and summarize the transformations algebraically. Real-world data sometimes show a linear relationship. If you calculate a line of best fit, then you can use it to make predictions about the data. In general, the study of relationships between variables is called regression. The absolute value of a number x, written |x|, represents its distance from zero on a number line. The value of x could be positive, negative, or zero, but its absolute value is always nonnegative. To solve an absolute value equation or inequality, you must consider each possibility. x= 4 X≥4 The distance from zero is 4. The distance is greater than or equal to 4. .... 654-3-2-10 1 2 3 4 5 6 x=-4ORx=4 x≤-4 OR x≥4 x≤ 4 The distance is less than or equal to 4. 2 3 4 x≥-4 AND x ≤ 4 Because an absolute value is never negative, the graph of the absolute-value function f(x) = [x) has two linear pieces that form a V shape with a vertex at (0, O). As shown at right, a variety of absolute-value functions can be created by transforming f(x) = |x|. (x) = 1x g(x) = |x + 31 The graph of g (x) = |x+31-5 is a translation of f (x) = |x| left 3 and down 5 © Houghton Milfin Harcourt Publishing Company 58 Holt McDougal Algebra