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:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

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:

$y-8=\dfrac{1-8}{0-(-9)}(x-(-9))$

$y-8=\dfrac{-7}{9}(x+9)$

$y-8=\dfrac{-7}{9}(x)+\dfrac{-7}{9}(9)$

$y-8=\dfrac{-7}{9}x-7$

Adding 8 on both sides, we get

$y-8+8=\dfrac{-7}{9}x-7+8$

$y=\dfrac{-7}{9}x+1$

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

$F(x)=\dfrac{-7}{9}x+1$

Therefore, the required linear function is $F(x)=\dfrac{-7}{9}x+1$.