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Section 5-1- Slope A. Definitions 1. Slope is the steepness of a line. 2. Slope is the vertical rise over the horizontal run. change in y (rise) 3. Slope = change in x (run) Ex 1: Determine the slope of each graph. a.) b.) 4. Formula for slope is m = ( y2 − y1 ) . ( x2 − x1 ) 5. Lines a. A vertical line has a slope that is undefined. b. A horizontal line has a slope of zero. Ex 2: Find the slope of the line that passes through (-3, 2) and (5, 5). Ex 3: Determine the slope of a line that passes through (2, -5) and (7, -10). Ex 4: Determine the value of r so that the line 3 through (r, 6) and (10, -3) has a slope of − . 2 HW: Algebra 5-1 p. 260-262 15-37 odd, 41-44, 50-52, 57, 59-60, 65-76, 77-85 odd Section 5-3 - Slope-Intercept form A. Slope-Intercept Form 1. The slope intercept form of an equation is y = mx + b , where m = slope and b = y-intercept. Ex 1: Write an equation whose slope is 2 and the yintercept is -5. Ex 2: Write the equation of the line in the graph. 2 Ex 3: Graph y = − x + 5 . 3 Ex 4: Graph 5 x + 4 y = 8 . HW: Algebra 5-3 p. 275-277 15-39 odd, 40-42, 45-46, 51-52, 58-60, 62-67 Section 5-4 Writing Equations in Slope-Intercept Form A. Write an equation given the Slope and One Point. Ex 1: Write an equation of the line that passes through (2, -3) with a slope of ½. (solve for b) y = mx + b B. Write an equation given two points. Ex 2: The table of ordered pairs shows the coordinates of two points on the graph of a function. Which equation describes the function? x y A. 5 y = 12 x − 16 -3 -4 B. y = 4 x − 16 -2 -8 C. y = −4 x + 16 D. y = −4 x − 16 Ex 3: In the middle of the 2004 season, Ichiro Suzuki was on track to break the single season hits record. After 36 games, he had 58 hits. After 128 games, Suzuki had 207 hits. Write a linear equation to estimate the number of hits for any number of games he played in. HW: Algebra 5-4 p. 284-285 11-33 odd, 40-43, 46-47, 49-50, 53-62 5-5 - Writing Equations in Point-Slope Form A. Point-slope Form 1. An equation can be written in point-slope form, which is y − y1 = m( x − x1 ) . Ex 1: Write the point-slope form of an equation that −3 passes through (-2, 0) with a slope of . 2 B. Forms of Linear Equations 1. Standard Form: Ax + By = C . 2. Slope-intercept form: y = mx + b . 3. Point-slope form: y − y1 = m( x − x1 ) . 5 Ex 2: Write y + 3 = − ( x − 2) in standard form. 4 4 Ex 3: Write y − 5 = ( x − 3) in slope-intercept form. 3 Ex 4: Write the equation of a line in slope intercept form that passes through (4, 3) and (6, -2). HW: Algebra 5-5 p. 289-291 15-51 odd, 55-57, 66, 72-87 Section 5-6 - Parallel and Perpendicular Lines A. Parallel lines 1. Two lines are parallel if they are in the same plane but do not intersect. 2. Parallel line have the same slope. Ex 1: Write the slope intercept form of an equation that passes through (4, -2) and is parallel to the graph 1 of y = x − 7 . 2 B. Perpendicular lines 1. Two lines are perpendicular if the product of their slopes is -1. Ex 2: Given A(5,5), B(8, 4), C(7, 1) and D(0, 0). Determine if AC ⊥ BD . Ex 3: Write the slope intercept form of an equation that passes through (4, -1) and is perpendicular to the graph of 7 x − 2 y = 3 . HW: Algebra 5-6 p. 296-297 13-37 odd, 42-44, 48-49, 50-54, 55-59 odd