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.
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.
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.
- 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.
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.