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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.
ExamplesExamples:
(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.
ExamplesExamples:
(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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