Question

5. Tracy recorded the chirps per second of the striped ground cricket at different temperatures. Using the recorded data shown, determine the equation that could be used to predict future counts (values rounded to two decimal places). X (chirps/ sec) Y (temperature °F) 14.4 76.3 15 79.6 15.5 75.2 16.2 83.3 17.1 80.6 18.4 84.3 20 88.6

Answer 1

To find the equation which would represent this problem, we have to use two points: (15, 79.6) and (18.4, 84.3).

First, we find the slope

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{84.3-79.6}{18.4-15}=\frac{4.7}{3.4}\approx1.38$

Now, we use the slope, one point, and the point-slope formula to find the equation

$\begin{gathered} y-y_1=m(x-x_1)_{} \\ y-84.3=1.38(x-18.4) \\ y-84.3=1.38x-25.392 \\ y=1.38x-25.392+84.3 \\ y=1.38x+58.908 \end{gathered}$

Therefore, an equation that approximates to the given values is y = 1.39x + 58.908.