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Algebra II Recipe: Slopes and Rates of Change
Determining Slopes of Lines
  1. slope - the ratio of vertical change (rise) to the horizontal change (run).
  2. formula for finding slope is m = (y2 - y1) / (x2 - x1)
    • Label the ordered pairs (x1, y1) and (x2, y2).
    • Substitute the values into the formula.
    • Simplify the fraction.
  3. A line rising from left to right has a positive slope.
  4. A line falling from left to right has a negative slope.
  5. A horizontal line has a slope of zero. When substituting any two points from a horizontal line into the formula gives 0/# = 0
  6. A vertical line has an undefined slope. When substituting any two points from a vertical line into the formula gives #/0, which is undefined.
  7. Parallel lines have the exact same slope.
  8. Slopes of perpendicular lines are opposites and reciprocals of each other, for example:
    4/3 and -(3/4).
  9. Steepness of Lines
    • If two lines have positive slopes, the line with the larger slope value is steeper.
    • If two lines have negative slopes, determine their absolute values. The line whose slope is the larger absolute is the steeper line.
ExamplesExamples:
Line 1 goes through (-3,3) and (3,-1)
Line 2 goes through (-2,-3) and (2,3)
Line 1 goes through (-3,1) and (3,4)
Line 2 goes through (-4,-3) and (4,1)



G Redden

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