Question

Write a linear function F with the values F(-9)=8 and F (0) =1

Answer 1

Given:

The values of a linear function are
`F(-9)=8` and
`F(0)=1`.

To find:

The linear function.

Solution:

If a linear function passes through two points, then the equation of the linear function is:

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

The values of a linear function are
`F(-9)=8` and
`F(0)=1`. It means the function passes through the points (-9,8) and (0,1). So, the equation of the linear function is:

`y-8=(1-8)/(0-(-9))(x-(-9))`

`y-8=(-7)/(9)(x+9)`

`y-8=(-7)/(9)(x)+(-7)/(9)(9)`

`y-8=(-7)/(9)x-7`

Adding 8 on both sides, we get

`y-8+8=(-7)/(9)x-7+8`

`y=(-7)/(9)x+1`

Putting
`y=F(x)`, we get

`F(x)=(-7)/(9)x+1`

Therefore, the required linear function is
`F(x)=(-7)/(9)x+1`.