Question

Write a linear function f with the given values: f(2) = 6 , f(5) = 18

Answer 1

`f(x)=4x-2`

Explanation:

A linear function has the following form:

`\begin{gathered} f(x)=mx+b \\ \text{ where m is the slope and b is y-intercept} \end{gathered}`

The value of the slope is calculated as follows:

`m=(f(x_2)-f(x_1))/(x_2-x_1)`

We calculate in this case, and we will obtain:

`m=(18-6)/(5-2)=(12)/(3)=4`

Now, the value of p, we can calculate it in the following way:

`\begin{gathered} f(x)=4x+b \\ 6=4\cdot2+b \\ b=6-8 \\ b=-2 \end{gathered}`

Therefore, the linear function would be:

`f(x)=4x-2`