Algebra II Recipe: Slopes and Rates of Change

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.