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.
Examples:
 (7, 2) & (1, 1)
 (3, -2) & (-1, -2)
 (6, -3) & (3, -1)
 (3, 0) & (3, -2)
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.
Examples:
 (1, 2) and m = -3/2
 (-4, 3) and m = 5
 (6, -2) and m = ¼
 (-3, -5) and m = -2

G Redden

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