Question 431096
Find an equation of the secant line containing (1, f(1)) and (2,f(2)). 
f(x) = x³ - x
<pre><font face = "consolas" color = "indigo" size = 4><b>

Let's calculate f(1)

f(x) = x³ - x
f(0) = 1³ - 1
f(0) = 0

So the point (1, f(1)) is the point (1,0)

Let's calculate f(2)

f(x) = x³ - x
f(2) = 2³ - 2
f(2) = 8 - 2
f(2) = 6

So the point (2, f(2)) is the point (2,6)

We plot those points:

{{{drawing(400,800,-5,5,-10,10, 

circle(1,0,.1), circle(2,6,.1), graph(400,800,-5,5,-10,10),
locate(2,6,"(2,6)"), locate(1.5,.5,"(1,0)")
)}}}

Next we draw the graph (in red) and the secant line (in green):

{{{drawing(400,800,-5,5,-10,10, 

circle(1,0,.1), circle(2,6,.1), graph(400,800,-5,5,-10,10,x^3-x),
locate(2,6,"(2,6)"), locate(1.3,.5,"(1,0)"), green(line(-3,-24,3,12))
)}}}

{{{m = (y[2]-y[1])/(x[2]-x[1])=(6-0)/(2-1)=6/1=6}}}

{{{y - y[1] = m(x-x[1])}}}

{{{y - 0 = 6(x-1)}}}
{{{y = 6x - 6}}}

That's the equation of the green secant line.

Edwin</pre>