Question

Students in a science class investigated how the speed of sound changes with the air temperature outside. The data are shown in the scatterplot Based on the scatterplot, what is the best prediction of the speed of sound when the air temperature is 50°C?

Answer 1

The behavior of the data are almost linear. Hence, a good prediction can be modeled by a straight line.

From the graph, we can take 2 points. For instance (0,333) and (40,354).

Hence, the slope of the approximate line is

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(354-333)/(40-0) \\ m=(21)/(40) \end{gathered}`

Then, the approximate line has the form

`y=(21)/(40)x+b`

where b is the y-intercept. This can be obtained by substituying the point (0,33) into the last equation, it yields

`\begin{gathered} 333=(21)/(40)(0)+b \\ b=333 \end{gathered}`

and the approximate line equation is

`y=(21)/(40)x+333`

By means of this equation we can predict another point. For instance, when the air temperature is x=50, we have

`\begin{gathered} y=(21)/(40)(50)+333 \\ y=(21\cdot50)/(40)+333 \\ y=26.25+333 \\ y=359.25 \end{gathered}`

Therefore, the best aproximation for the speed of sound is y=360 m/s