Question

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

Answer 1

ANSWER:

$f(x)=4x-2$

STEP-BY-STEP 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:

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

We calculate in this case, and we will obtain:

$m=\frac{18-6}{5-2}=\frac{12}{3}=4$

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:

$f(x)=4x-2$