Let's look at the definition of a secant line:

In geometry, a secant of a curve is a line that intersects the curve in at least two points. The word secant comes from the Latin word secare, meaning to cut.

So, imagine a line in the plane, and then further imagine two points on that line and a line though those two points. Can you see that the secant line will coincide with the original line?

Consider the linear function:

$\displaystyle f(x)=ax+b$

Now, consider two arbitrary points on this linear function:

$\displaystyle (x,f(x))=(x,ax+b)$

$\displaystyle (x+h,f(x+h))=(x+h,a(x+h)+b)$

And so the slope $\displaystyle m$ of the secant line is given by:

$\displaystyle m=\frac{f(x+h)-f(x)}{(x+h)-(x)}=\frac{(ax+ah+b)-(ax+b)}{h}=a$

Then using the point slope formula, we find the equation of the secant line to be:

$\displaystyle y=a(x-x)+f(x)=f(x)$

Thus, we find the secant line does in fact coincide with the original line.