It supposes that is linear, and draws a secant line that passes through and . However, unlike the Newton method and other methods (like the bisection method), the interval and must not necessarily contain a root.
With the help of this image, we can visualise that:
…and from there:
Finally, in general, we have that:
Notice that, if the function was linear, the secant line would intersect the axis exactly on the root.
However, since is rarely linear, the intersection of the secant line will not be the root, but it will be close.