252 Chapter 3 Graphing Linear Equations in Two Variables Graphing a Line from Its Slope and y-Intercept y 4x Example 4 Graph the equation of the line by using the slope and y-intercept. Solution: The equation can be written as Therefore, we can plot the y-intercept at (0, 0). The slope m 4 can be written as m 4 1 y 4x 0. The change in y is 4. The change in x is 1. y Start here (0, 0) 1 2 3 4 5 54 321 5 4 3 2 1 1 2 3 4 5 Figure 3-29 To find a second point on the line, start at the y-intercept and move up 4 units and to the right 1 unit. Then draw the line through the two points (Figure 3-29). 3. Determining Whether Two Lines Are Parallel, Perpendicular, or Neither x The slope-intercept form provides a means to find the slope of a line by inspection. Recall that if the slopes of two lines are known, then we can compare the slopes to determine if the lines are parallel, perpendicular, or neither parallel nor perpendicular. (Two distinct nonvertical lines are parallel if their slopes are equal. Two lines are perpendicular if the slope of one line is the opposite of the reciprocal of the slope of the other line.) Determining If Two Lines Are Parallel, Perpendicular, or Neither Example 5 For each pair of lines, determine if they are parallel, perpendicular, or neither. a. l1: y 3x 5 b. l2: y 3x 1 l1: y 32 l2: y 23 x 2 x 1 Solution: a. l1: y 3x 5 The slope of l1 is 3. l2: y 3x 1 The slopeof l2 is 3. Because the slopes are the same, the lines are parallel. 32 l1: y 32 b. The slope of l1 is . 23 The slope of l2 is . l2: y 23 x 2 x 1 The slopes are not the same.Therefore, the lines are not parallel.The values of the slopes are reciprocals, but they are not opposite in sign.Therefore, the lines are not perpendicular.The lines are neither parallel nor perpendicular. Skill Practice 7. Graph the equation by using the slope and the y-intercept. y Skill Practice For each pair of lines determine if they are parallel, perpendicular, or neither. 8. 9. y 3x 5 y 3x 15 y y Answers 7. x x 5 4 3 2 1 1 2 1 2 y 1 4 x 5 6 5 6 54 3 1 2 3 4 5 2 1 1 2 3 4 5 8. Neither 9. Parallel x Classroom Example: p. 258, Exercise 54 Classroom Examples: p. 258, Exercises 60 and 62
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