Question

To begin deriving the equation of the line y = 6x, Matt drew a triangle with vertices (0,0), (1,0), and (1,6). A similar triangle with which of these vertices would allow him to continue with his derivation?

Answer 1

In this case we have that y = 6x, then the triangle that you need to do is the one with vertices at:

(0,0) , (x,0) , (x, y(x))

in this case, Matt used x = 1, and y(x) = 6*1= 6

then we have that the vertices are:

(0,0), (x, 0), (x, y(x))

but if you use other value of x you can find another triangle that also can be usefull to find the derivate:

x = 2

the vertices will be:

(0,0), (2,0), (2, 2*6 = 12)

now, you can find the slope (and the tangent line = derivate) by the equation:

f' = (y(2) - y(1))/( 2- 1)