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The slope m of a nonvertical line is the number of units the line rises or falls for each unit of horizontal change

F INDING THE S LOPE OF A L INE. The slope m of a nonvertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. F INDING THE S LOPE OF A L INE. nonvertical line. y. 9 7 5 3 1. The slanted line at the right rises

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The slope m of a nonvertical line is the number of units the line rises or falls for each unit of horizontal change

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  1. FINDING THE SLOPE OF A LINE The slopem of a nonvertical line is the number of units the line rises or falls for each unit of horizontal change from left to right.

  2. FINDING THE SLOPE OF A LINE nonvertical line y 9 7 5 3 1 The slanted line at the right rises 3 units for each 2 units of horizontal change from left to right. So, the slope m of the line is . (2, 5) 3 2 rise = 5 - 2 = 3 units (0, 2) run = 2 - 0 = 2 units - 1 1 3 5 7 9 x -1 rise run 5 - 2 3 = The slopem of a nonvertical line is the number of units the line rises or falls for each unit of horizontal change from left to right. Two points on a line are all that is needed to find its slope. slope = = 2 - 0 2

  3. FINDING THE SLOPE OF A LINE (x1,y1) (x1,y1) y (x2,y2) (x2,y2) (x2, y2) (x1, y1) (y2 - y1) (x2 - x1) x rise change in y = x2-x1 run change in x y2-y1 The slope m of the nonvertical line passing through the points(x1, y1) and(x2, y2)is Read y1 as “y sub one” Read x1 as “x sub one” m = =

  4. FINDING THE SLOPE OF A LINE y2-y1 m = x2-x1 rise change in y y2-y1 m = = = run change in x x2-x1 the numerator and denominator must use the same subtraction order. numerator denominator y2-y1 CORRECT Subtraction order is the same x2-x1 y2-y1 INCORRECT Subtraction order is different x1-x2 When you use the formula for the slope, The order of subtraction is important. You can label either point as(x1, y1) and the other point as (x2, y2). However, both the numerator and denominator must use the same order.

  5. A Line with a Zero Slope is Horizontal line (3,2). (3,2). (-1,2) (-1, 2) y (-1,2) 9 7 5 3 1 (x1,y1) Let (x1, y1) = (-1, 2) and (x1,y1) (-1,2) (x2, y2) = (3, 2) (x2,y2) (x2,y2) (3,2) (3,2) y2 - y1 Rise: difference of y-values rise = 2 - 2 = 0 units x2 - x1 Run: difference of x-values (-1,2) (3,2) 2 - 2 = 3 - (-1) run = 3 - ( -1) = 4 units 0 4 Simplify. = -1 1 3 5 7 9 x -1 = 0 Slope is zero. Line is horizontal. Find the slope of a line passing through (-1, 2) and (3, 2). SOLUTION m= Substitute values.

  6. Slope as a Rate of Change (0,2500) h = 2500 feet h = 2500 feet t = 0 seconds, t = 0 seconds, t = 35 seconds, t = 35 seconds, h = 2115 feet. h = 2115 feet. y 2700 2500 2300 2100 1900 (35,2115) Height (feet) x 5 15 25 35 45 Time (seconds) INTERPRETING SLOPE AS A RATE OF CHANGE You are parachuting. At time t = 0 seconds, you open your parachute at h = 2500 feet above the ground. At t = 35 seconds, you are at h = 2115 feet. a. What is your rate of change in height? b. About when will you reach the ground?

  7. Slope as a Rate of Change rate of change. change in time change in height Change in Height Rate of Change = Change in Time m - 385 LABELS 35 - 385 ALGEBRAIC MODEL = = m 35 Your rate of change is -11 ft/sec. The negative value indicates you are falling. SOLUTION a. Use the formula for slope to find the rate of change. The change in time is 35 - 0 = 35 seconds. Subtract in the same order. The change in height is 2115 - 2500 = -385 feet. VERBAL MODEL Rate of Change = m(ft/sec) Change in Height =- 385 (ft) Change in Time = 35 (sec) -11

  8. Slope as a Rate of Change Distance = Time Time Distance Rate Time -2500 ft = 227 sec -11 ft/sec You will reach the ground about 227 seconds after opening your parachute. b. Falling at a rate of -ll ft/sec, find the time it will take you to fall 2500 ft. Rate

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