How to Determine the Y-Intercept of a Trend Line

How to Determine the Y-Intercept of a Trend Line
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You may need to determine the y-intercept of a trend line in order to understand more about the data that the trend line is representing. A trend line is a line that is drawn above, below or through various data points in order to show their general direction. The trend line may be drawn from the upper left corner to the lower right corner, indicating that the data have a negative slope, or from the lower left corner to the upper right corner, indicating that the data have a positive slope. The y-intercept of the trend line is the point at which the trend line has an x value of zero.

    Examine the trend line that is on the graph. One of the methods for determining the y-intercept is through observation. Find the x-axis, or horizontal axis on the graph, and locate the value at which x = 0. Place your pencil over this point. Follow the vertical line above this point with your pencil until the pencil intersects the trend line. Look at the y-axis, or vertical axis, and find the value for which this intersection occurs. This value is the y-intercept.

    Compare the general equation of a line to the equation of the trend line. The general formula for a line is:


    for which m is the slope, b is the y-intercept, x is any x value and y is any y value. By looking at the equation of the trend line, you can determine the y-intercept. For example, if the equation of the trend line is y=2x+5, the y-intercept is 5. You would receive this same answer if you let x = 0.

    Review the point-slope formula. If the trend line does not have an equation, then you will want to create one in order to determine the y-intercept. The point-slope formula is:


    where m is the slope, y1 is the y coordinate and x1 is the x coordinate.

    Find the slope of the line. In order to generate the equation of the line, you need to find the slope. The equation of the slope is:


    where x1 and y1 are one set of coordinates on the trend line and x2 and y2 are another set of coordinates on the trend line. For example, two points on the trend line may be (2,9) and (3,11). Putting these points into the equation, you get:


    You should calculate an answer of m = 2.

    Find another point on the trend line and put the values of the point and the slope into the point-slope formula. For example, if the point is (1,7) and the slope is m = 2, you get:


    Solving for y, you receive the equation


    Therefore, the y-intercept of the trend line is 5.

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