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

User Lukasz M
by
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1 Answer

22 votes
22 votes

ANSWER:


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

User Nunser
by
2.9k points
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