Algebra I Recipe: The Slope of a Line

A. Slope Facts

1. Positive slope – when the line slants upward from left to right.
2. Negative slope – when the line slants downward from left to right.
3. There are two directions or changes with slope.
• 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.
4. The slope formula is m = (y₂ - y₁) / (x₂ - x₁) and used when you know two points on the line.
• 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.
5. A horizontal line with equation y = # has a slope of zero.
• 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.
6. A vertical line with equation x = # has no slope or undefined slope.
• 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)

1. Pick any two points on the line.
2. Determine the rise by counting the spaces you move up or down.
• Move up – positive number
• Move down – negative number
3. Determine the run by counting the spaces you move right or left.
• Move right – positive number
• Move left – negative number

C. How to Graph a Line with a Given Slope and a Given Point the Line Goes Through

1. Graph the given point.
2. Use the movements of slope (or rise/run) from the graphed point.
3. Make a point after making the two movements and repeat to graph more points.

Practice Problems