How do you find the equation of a secant line?

A secant line of a curve is a straight line connecting two points on the curve. The equation for a line is given by the formula y = mx + b, where m equals the slope of the line, and b equals the y intercept, or the point where the line crosses the y axis. Find the equation by first finding the slope, then plugging values for x and y into the formula and solving for b.

1. Find two points on the secant

   For example, assume that you are given the function y = x^2 and asked to find the equation for the secant line connecting the points at x = 1 and x = 3. At x = 1, y = 1^2 or 1. At x = 3, y = 3 ^2 or 9. That means the two points that define the secant are (1, 1) and (3, 9).

2. Find the slope of the secant

   The slope of a line is equal to rise over run, or change in y over change in x. It is found by subtracting one y coordinate from the other, then subtracting one x coordinate from the other, and dividing change in y by change in x. In the example given, 9 - 1 = 8 and 3 - 1 = 2. Dividing 8 by 2 equals 4, so the slope of the line is 4.

3. Plug in values to find the y intercept

   Plugging values into the equation y = mx + b for one of the points, say (3, 9), yields the equation 9 = 4 (3) + b. Solving for b gives the equation b = 9 - 12, which equals -3. That means the line crosses the y axis at -3, so the equation for the secant line is y = mx - 3.