NAME DATE PERIOD 2-4 Study Guide and Intervention (continued) Writing Linear Equations Parallel and Perpendicular Lines Use the slope-intercept or point-slope form to find equations of lines that are parallel or perpe or perpendicular to a given line. Remember that parallel lines have equal slope. The slopes of two perpendicular lines are negative reciprocals, that is, their product is -1. Example 1 Write an equation of the Example 2 Write an equation of line that passes through (8, 2) and is the line that passes through (-1, 5) and perpendicular to the line whose is parallel to the graph of y = 3x + 1. equation is y = - 2 x + 3. The slope of the given line is 3. Since the The slope of the given line is -2. Since the slopes of parallel lines are equal, the slope slopes of perpendicular lines are negative of the parallel line is also 3. reciprocals, the slope of the perpendicular Use the slope and the given point to write line is 2. the equation. Use the slope and the given point to write y -y1 = m( x - x ) Point-slope form the equation. y - 5= 3(x - (-1)) ( x, , y,) = (-1, 5), m = 3 y - y1 = m(x - x]) Point-slope form y - 5 = 3x + 3 Distributive Prop. y - 2 = 2(x - 8) ( x,, y1) = (8, 2), m= 2 y = 3x + 8 Add 5 to each side. y - 2 = 2x - 16 Distributive Prop. An equation of the line is y = 3x + 8. y = 2x - 14 Add 2 to each side. An equation of the line is y = 2x - 14. Exercises Write an equation in slope-intercept form for the line that satisfies each set of conditions. XIVI 1. passes through (-4, 2), parallel to y = 2x + 5 \\= 2x+ 2. passes through (3, 1), perpendicular to y = -3x + 2 y= 3x-8 3. passes through (1, -1), parallel to the line that passes through (4, 1) and (2, -3) 4. passes through (4, 7), perpendicular to the line that passes through (3, 6) and (3, 15) 5. passes through (8, -6), perpendicular to 2x - y = 4 6. passes through (2, -2), perpendicular to x + 5y = 6 7. passes through (6, 1), parallel to the line with x-intercept -3 and y-intercept 5 8. passes through (-2, 1), perpendicular to y = 4x - 11 Chapter 2 20 Glencoe Algebra