How Do We Write the Equation of a Horizontal Line?

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Any straight line on an x- and y-coordinate graph can be described using the equation y = mx + b. The x and y term refer to a specific coordinate point on the graphed line. The m term refers to the slope of the line or the change in the y-values with respect to the x-values (rise of the graph/ run of the graph). The b term indicates the y-intercept or point, or where the line intersects the y-axis. Using this equation and knowledge of the meaning of each term in the general equation, you can easily determine the equation of a horizontal line or any other straight line.

    Identify the y-intercept. For example, a horizontal line that crosses the y-axis at 2 would have a y-intercept of 2. So plug a "2" into your equation, yielding y = mx + 2.

    Determine the slope of the graph. In a graph that has grids, you can count how many squares up (rise) and over to the right (run) a point on a line is from another point on the same line. For example, a line that has a slope of 1/2 would have all points to the right of any point be one count up and two counts over to the right. You can also find the slope through the equation m = (y2 - y1)/(x2 - x1) by plugging in the values of two points on the line, (x1, y1) and (x2, y2). In the example, a horizontal line that has a y-intercept of 2 would have a slope (m) = 0. Because it is horizontal, there is no change in y (rise) with respect to x (run).

    Write the final equation of the line. In the example, substituting the calculated values of m and b yields y = 0*x + 2 or y = 2. The general equation is always written with x and y as variables to describe the line. Do not substitute any numbers in for x and y when writing the general equation of the line.

    Tips

    • For any horizontal line, the general equation will always be y = b (y-intercept) because a horizontal line does not have slope. The procedure in the steps, however, can be used to find the general equation of any straight line.

References

About the Author

Matt Perdue is a medical student at an allopathic U.S. medical school. Beginning in 2010, he began writing science-related articles for eHow. He was also authored a paper for a medical journal exploring current recommendations for bone scans to diagnose osteoporosis.

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