Question

Don’t really know what linear functions are

Answer 1

The rate of change of f(x) is greater than that of g(x)

They have the same y intercept of 14

Explanation:

Given

`g(x) = -(1)/(2)x + 14`

Table for function f(x)

Required

Compare their rate of change and intercept

For g(x), we have:

`g(x) = -(1)/(2)x + 14`

The form of an equation is:

`y = mx + b`

Where

`m = slope`

`b =y\ intercept`

So:

`m = -(1)/(4)`

`b = 14`

For f(x): Start by calculating the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (17-16)/(6-4)`

`m = (1)/(2)`

The intercept is calculated using:

`m = (y_2 - y_1)/(x_2 - x_1)`

Where

`(x_1,y_1) = (-2,13)`

`(x_2,y_2) = (0,y)` --- we want to solve for y

So:

`(1)/(2) = (y - 13)/(0 --2)`

`(1)/(2) = (y - 13)/(2)`

Multiply both sides by 2

`1 =y - 13`

Make y the subject

`y =1 + 13`

`y = 14`

So, we have:

`m = -(1)/(4)` and
`b = 14` -- for g(x)

`m = (1)/(2)` and
`y = 14` --- for f(x)

By comparison:

The rate of change (i.e. slope) of f(x) is greater than that of g(x) because
`1/2 > -1/2`

They have the same y intercept of 14