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= (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= (800-0)/(80-0) = (800)/(80) =10`


Give function g(x), passing through points (2, -6) and (4, 12), the slope is given by

`m= (12-(-6))/(4-2) = (12+6)/(2) = (18)/(2) =9`

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