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} 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

`(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)`

Using the points (32, 0) and (41, 5), we have:

`(y-0)/(x-32) = (5-0)/(41-32)= (5)/(9) \\ \\ \Rightarrow y=(5)/(9)(x-32)`