Question

Write a linear function f with the given values f(10)=5 , f(2)= -3

Answer 1

The linear function is

`f(x)=x-5`

Explanation:

Given values:

`f(10)=5`

`f(2)=-3`

From the given values, we can identify the points on the line.

For
`f(x)=y` point can be given as
`(x,y)`

So, the points are:

`(10,5)` and
`(2,-3)`

Using the points we can find slope of the line
`m`.

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

`m=(-3-5)/(2-10)`

`m=(-8)/(-8)`

∴
`m=1`

Using point slope equation to find equation of line.

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

where
`(x_1,y_1)` is a point on line.

Using point (10,5) and slope
`m=1` to find equation of line.

`y-5=1(x-10)`

Simplifying.

`y-5=x-10`

Adding 5 both sides.

`y-5+5=x-10+5`

`y=x-5`

So, the function can be written as:

`f(x)=x-5` [ ∵
`y=f(x)` ]