Determining Slopes of Lines
slope - the ratio of vertical change (rise) to the horizontal change (run).
- formula for finding slope is m = (y2 - y1) / (x2 - x1)
A line rising from left to right has a positive slope.
A line falling from left to right has a negative slope.
A horizontal line has a slope of zero. When substituting any two points from a horizontal line into the formula gives 0/# = 0
A vertical line has an undefined slope. When substituting any two points from a vertical line into the formula gives #/0, which is undefined.
Parallel lines have the exact same slope.
Slopes of perpendicular lines are opposites and reciprocals of each other, for example:
- Label the ordered pairs (x1, y1) and (x2, y2).
- Substitute the values into the formula.
- Simplify the fraction.
4/3 and -(3/4).
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.