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
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{354-333}{40-0} \\ m=\frac{21}{40} \end{gathered}[/tex]Then, the approximate line has the form
[tex]y=\frac{21}{40}x+b[/tex]where b is the y-intercept. This can be obtained by substituying the point (0,33) into the last equation, it yields
[tex]\begin{gathered} 333=\frac{21}{40}(0)+b \\ b=333 \end{gathered}[/tex]and the approximate line equation is
[tex]y=\frac{21}{40}x+333[/tex]By means of this equation we can predict another point. For instance, when the air temperature is x=50, we have
[tex]\begin{gathered} y=\frac{21}{40}(50)+333 \\ y=\frac{21\cdot50}{40}+333 \\ y=26.25+333 \\ y=359.25 \end{gathered}[/tex]Therefore, the best aproximation for the speed of sound is y=360 m/s
