Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Lesson 2-4 NAME DATE PERIOD Chapter 2 23 Glencoe Algebra 2 Forms of Equations Write an equation in slope-intercept form for the line that has slope -2 and passes through the point (3, 7). Substitute for m, x, and y in the slope-intercept form. y = mx + b Slope-intercept form 7 = (-2)(3) + b (x, y) = (3, 7), m = -2 7 = -6 + b Simplify. 13 = b Add 6 to both sides. The y-intercept is 13. The equation in slope-intercept form is y = -2x + 13. Write an equation in slope-intercept form for the line that has slope 1 − 3 and x-intercept 5. y = mx + b Slope-intercept form 0 = ( 1 − 3 ) (5) + b (x, y) = (5, 0), m = 1 − 3 0 = 5 − 3 + b Simplify. - 5 − 3 = b Subtract 5 − 3 from both sides. The y-intercept is - 5 − 3 . The slope-intercept form is y = 1 − 3 x - 5 − 3 . Exercises Write an equation in slope-intercept form for the line described. 1. slope -2, passes through (-4, 6) 2. slope 3 − 2 , y-intercept 4 3. slope 1, passes through (2, 5) 4. slope - 13 − 5 , passes through (5, -7) Write an equation in slope-intercept form for each graph. 5. 6. 7. x y O (1, 6) (3, 0) 2 2 4 6 8 -2 4 6 8 x y O (4, 5) (0, 0) 2 2 4 6 8 -2 -2 4 6 8 x y O (-4, 1) (5, 2) 2 -2 -4 2 4 -2 -4 4 6 Slope-Intercept Form of a Linear Equation y = mx + b, where m is the slope and b is the y-intercept Point-Slope Form of a Linear Equation y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and m is the slope of the line Study Guide and Intervention Writing Linear Equations 2-4 Example 1 Example 2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME DATE PERIOD Chapter 2 24 Glencoe Algebra 2 Parallel and Perpendicular Lines Use the slope-intercept or point-slope form to find equations of lines that are parallel 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. Write an equation of the line that passes through (8, 2) and is perpendicular to the line whose equation is y = - 1 − 2 x + 3. The slope of the given line is - 1 − 2 . Since the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line is 2. Use the slope and the given point to write the equation. y - y1 = m(x - x1) Point-slope form y - 2 = 2(x - 8) (x1, y1) = (8, 2), m = 2 y - 2 = 2x - 16 Distributive Prop. y = 2x - 14 Add 2 to each side. An equation of the line is y = 2x - 14. Write an equation of the line that passes through (-1, 5) and is parallel to the graph of y = 3x + 1. The slope of the given line is 3. Since the slopes of parallel lines are equal, the slope of the parallel line is also 3. Use the slope and the given point to write the equation. y -y1 = m(x - x1) Point-slope form y - 5 = 3(x - (-1)) (x1, y1) = (-1, 5), m = 3 y - 5 = 3x + 3 Distributive Prop. y = 3x + 8 Add 5 to each side. An equation of the line is y = 3x + 8. Exercises Write an equation in slope-intercept form for the line that satisfies each set of conditions. 1. passes through (-4, 2), parallel to y = 1 − 2 x + 5 2. passes through (3, 1), perpendicular to y = -3x + 2 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 Study Guide and Intervention (continued) Writing Linear Equations 2-4 Example 1 Example 2 uploads/Management/ study-guide 30 .pdf
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