AlgebraLab

Algebra II Recipe: Slopes and Rates of Change

By G Redden

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, such as ¾ and -¾.
  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.
Find the slopes to determine if the lines are parallel or perpendicular.
1.
Line 1 goes through (-3,3) and (3,-1)
Line 2 goes through (-2,-3) and (2,3)
2.
Line 1 goes through (-3,1) and (3,4)
Line 2 goes through (-4,-3) and (4,1)