Section 3.4 Slope-Intercept Form of a Linear Equation 253 Determining If Two Lines Are Parallel, Perpendicular, or Neither For each pair of lines, determine if they are parallel, perpendicular, or neither. a. l1: x 3y 9 b. l1: x 2 l2: 3x y 4 l2: 2y 8 Solution: a. First write the equation of each line in slope-intercept form. l1: x 3y 9 l2: 3x y 4 3y x 9 3x y 4 3y y 3x 4 3 y 1 3 l1: y . 13 The slope of The slope of l2: y 3x 4 l2 is 3. 3 13 The slope of is the opposite of the reciprocal of .Therefore, the lines are perpendicular. b. The equation represents a vertical line because the equation is in the form The equation can be simplified to which represents a horizontal line. In this example, we do not need to analyze the slopes because vertical lines and horizontal lines are perpendicular. 4. Writing an Equation of a Line Using Slope-Intercept Form The slope-intercept form of a linear equation can be used to write an equation of a line when the slope is known and the y-intercept is known. Writing an Equation of a Line Using Slope-Intercept Form Write an equation of the line whose slope is and whose y-intercept is (0, 8). Solution: The slope is given as , and the y-intercept (0, b) is given as (0, 8). Substitute the values into slope-intercept form. y mx b y 2 3 x 8 m 23 and b 8 m 23 2 3 Example 7 2y 8 y 4, x k. x 2 l1 is 13 x 3 x 3 x 3 9 3 Example 6 Skill Practice For each pair of lines, determine if they are parallel, perpendicular, or neither. 10. 11. x 5y 10 5x 1 y y 5 x 6 Classroom Examples: p. 258, Exercises 64 and 68 Skill Practice 12. Write an equation of the line whose slope is and y-intercept is 10, 102. Classroom Example: p. 258, Exercise 74 Answers 10. Perpendicular 11. Perpendicular 12. y 4x 10 4
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