Question

Consider the two functions below. Which one of these functions is linear? What is its equation? Enter any answers to two decimal places.

Answer 1

`y = 1.67x`

Explanation:

Function A:

x || 3 || 6 || 9 || 12 || 15

y || 5 || 10 || 15 || 20 || 25

See attachment for Function B

First, we need to determine the equation of function A using linear interpolation

As follows:

`y = y_1 + (x - x_1)(y_2 - y_1)/(x_2 - x_1)`

Take any two corresponding values of x and y to be:

`(x_1,y_1) = (3,5)`

`(x_2,y_2) = (15,25)`

The equation becomes:

`y = y_1 + (x - x_1)(y_2 - y_1)/(x_2 - x_1)`

`y = 5 + (x - 3)(25 - 5)/(15 - 3)`

`y = 5 + (x - 3)(20)/(12)`

`y = 5 + (x - 3)(5)/(3)`

Open bracket

`y = 5 + (5x)/(3) - (5*3)/(3)`

`y = 5 + (5x)/(3) - 5`

Collect Like Terms

`y = (5x)/(3) - 5 + 5`

`y = (5x)/(3)`

`y = 1.67x`

This function is linear and there is no need to check for function B