Question

Write a linear function f with the values f(-1) = -3 and f (2) = 6. A function is f(x) =

Answer 1

The linear equation is;

`f(x)=3x`

Step-by-step explanation:

Given that the function f(x) is a linear function;

`f(x)=mx+b`

let us derive the values of m and b.

At x=-1, f(-1)=-3;

`\begin{gathered} f(-1)=m(-1)+b=-3 \\ -m+b=-3\text{ --------1} \end{gathered}`

At x=2, f(2)=6;

`\begin{gathered} f(2)=m(2)+b=6 \\ 2m+b=6\text{ ---------2} \end{gathered}`

subtract equation 1 from 2;

`\begin{gathered} 2m-(-m)+b-b=6-(-3) \\ 3m=9 \\ m=(9)/(3) \\ m=3 \end{gathered}`

let's substitute the value of m into equation 2;

`\begin{gathered} 2m+b=6 \\ 2(3)+b=6 \\ 6+b=6 \\ b=6-6 \\ b=0 \end{gathered}`

Therefore, since we have the values of m and b we can substitute to get the equation f(x);

`\begin{gathered} f(x)=mx+b \\ f(x)=3x+0 \\ f(x)=3x \end{gathered}`

The linear equation is;

`f(x)=3x`