How to Figure Out the Slope of a Line

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A line can be graphed on a set of coordinate axes with a horizontal x-axis and a vertical y-axis. The points on the graph are designated by coordinates in the form of (x, y). The slope of a line measures how the line slants in relation to the axes. A positive slope slants up and to the right. A negative slope slants down and to the right. A zero slope means a line is horizontal. A vertical line has an undefined slope. Determine the slope of a line using the slope formula or by identifying “m” in the slope-intercept form of a line’s equation, which is y = mx + b.

Figuring Slope from Two Points on a Line

    Input the corresponding x and y points into the slope formula m = (y2 - y1)/(x2 - x1) for a line that contains the two points (x1, y1) and (x2, y2). For example, the slope formula for a line that contains the two points (2, 3) and (4, 9) is m = (9 - 3)/(4 - 2).

    Subtract 3 from 9 to calculate the numerator: 9 minus 3 equals 6.

    Subtract 2 from 4 to calculate the denominator: 4 minus 2 equals 2. This leaves the equation m = 6/2.

    Divide the numerator by the denominator to solve for m, which is the slope of the line: 6 divided by 2 equals 3. The slope of the line is 3.

Figuring Slope from a Line’s Equation

    Subtract 4x from both sides of the example line equation 4x + 2y = 8 to isolate 2y on the left side of the equation. This equals 4x - 4x + 2y = -4x + 8, or 2y = -4x + 8.

    Divide both sides of the equation by 2 to reduce 2y to y. This equals 2y/2 = (-4x + 8)/2, or y = -2x + 4. This is the line’s equation rearranged into the slope-intercept form.

    Identify m in the equation’s slope-intercept form y = -2x + 4, which is -2. This is the line’s slope.

References

Photo Credits

  • Ryan McVay/Photodisc/Getty Images

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