Question

A manufacturer earns Rs4500 in the first month and Rs 6000 in second month. On plotting these points a manufacturer observes a linear function. Find the linear function that fits in data?

Answer 1

`f(x) = 1500x +3000`

Explanation:

Given

Represent the months with x and the earnings with y.

So:

`(x_1,y_1) = (1,4500)`

`(x_2,y_2) = (2,6000)`

Required

Determine the linear function

First, calculate slope (m)

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

`m = (6000 - 4500)/(2 - 1)`

`m = (1500)/(1)`

`m = 1500`

The equation is then calculated using:

`y = m(x - x_1) + y_1`

`y = 1500(x - 1) + 4500`

`y = 1500x - 1500 + 4500`

`y = 1500x +3000`

As a function, we have:

`f(x) = 1500x +3000`