A. Slope Facts
- Positive slope – when the line slants upward from left to right.
- Negative slope – when the line slants downward from left to right.
- There are two directions or changes with slope.
The slope formula is m = (y2 - y1) / (x2 - x1) and used when you know two points on the line.
- The up and down change or vertical change is the change in the y-values.
- The left and right change or horizontal change is the change in the x-values.
A horizontal line with equation y = # has a slope of zero.
- Label the points (x1, y1) & (x2, y2).
- Substitute the numbers into the formula.
- Perform the operation in the numerator and denominator.
- Reduce the fraction completely.
- DO NOT write slope as a mixed number.
A vertical line with equation x = # has no slope or undefined slope.
- The y-values would be the same therefore zero would be obtained in the numerator of the formula.
- Zero divided by any number equals zero.
- The x-values would be the same therefore zero would be obtained in the denominator of the formula.
- Any number divided by zero is undefined.
B. How to Determine the Slope of a Graphed Line Using (rise)/(run)
C. How to Graph a Line with a Given Slope and a Given Point the Line Goes Through
- Pick any two points on the line.
- Determine the rise by counting the spaces you move up or down.
Determine the run by counting the spaces you move right or left.
- Move up – positive number
- Move down – negative number
- Move right – positive number
- Move left – negative number
- Graph the given point.
- Use the movements of slope (or rise/run) from the graphed point.
- Make a point after making the two movements and repeat to graph more points.