Question

Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x) Dawn writes 800 pages in 80 days. x g(x) 2 −6 4 12 6 30

Answer 1

Given function f(x) which is described by "Dawn writes 800 pages in 80 days".

From this function we can notice that Dawn writes 0 pages in 0 days, (i.e. the initial point of the function is point (0, 0).

Recall that the slope, m, of a line passing through points:
$(x_1,y_1)$ and $(x_2,y_2)$
is given by
$m= \frac{y_2-y_1}{x_2-x_1}$

Function f(x) passes through points (0, 0) and (80, 800).

Thus the slope of function f(x) is given by
$m= \frac{800-0}{80-0} = \frac{800}{80} =10$


Give function g(x), passing through points (2, -6) and (4, 12), the slope is given by
$m= \frac{12-(-6)}{4-2} = \frac{12+6}{2} = \frac{18}{2} =9$

It can be seen that the slope of f(x) and the slope of g(x) are close.