Question

Find the linear function with the following properties.f( -4)= 7f( -8)= - 2answer : f (x) = ?

Answer 1

its one-half

Explanation:

tested

Answer 2

First, we find the slope

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

Where,

`\begin{gathered} x_1=-4 \\ x_2=-8 \\ y_1=7 \\ y_2=-2 \end{gathered}`
`m=(-2-7)/(-8-(-4))=(-9)/(-8+4)=-(9)/(-4)=(9)/(4)`

Then, we use the point-slope formula to find the equation

`\begin{gathered} y-y_1=m(x-x_1) \\ y-7=(9)/(4)(x-(-4)) \\ y-7=(9)/(4)x+9 \\ y=(9)/(4)x+9+7 \\ y=(9)/(4)x+16 \end{gathered}`

Hence, the function is

`f(x)=(9)/(4)x+16`