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.
Examples:
 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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