Genesis Gibbs

## Answered question

2022-10-09

Find a formula for the linear function whose data is given in the table below.
$\begin{array}{|llll|}\hline \text{Year, t}& 0& 4& 8\\ \text{Value of a computer, V}& 1900& 1620& 1340\\ \hline\end{array}$

### Answer & Explanation

Krha77

Beginner2022-10-10Added 8 answers

A linear function is a function whose graph produces a line. Linear functions can always be written in the form f(x) = b + mx or f(x) = mx + b; they’re equivalent, where b is the initial or starting value of the function (when input, x = 0), and m is the constant rate of change of the function.
Here x corresponds to year (t) and y correesponds to value of computer.
Lets us choose two points (0,1900) and (4,1620) and substitute in the general equation.

Again,
$1620=1900+m\left(4\right)\phantom{\rule{0ex}{0ex}}-280=4m\phantom{\rule{0ex}{0ex}}m=-70$
Therefore,
$f\left(x\right)=1900-70x$
Thus the linear function is,
$V\left(t\right)=1900-70t$

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