Question

The table below gives data from a linear function. find a formula for the function.

Answer 1

Given the following table that gives data from a linear function:

$\begin {tabular} {|c|c|c|c|} Temperature, y = f(x) (^\circ C)&0&5&20 \\ [1ex] Temperature, x (^\circ F)&32&41&68 \\ \end {tabular}$

The formular for the function can be obtained by choosing two points from the table and using the formular for the equation of a straight line.

Recall that the equation of a straight line is given by
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Using the points (32, 0) and (41, 5), we have:
$\frac{y-0}{x-32} = \frac{5-0}{41-32}= \frac{5}{9} \\ \\ \Rightarrow y=\frac{5}{9}(x-32)$