Chapter 5.7, Problem 2LC

To determine

To graph: Trend line and write the equation of the given table.

Explanation of Solution

Given information: data provided in the question that are used to draw the trend line is

  

Here in the table $x_1$ is the latitude and $y_1$ is the temperature in January.

Graph: the trend line is shown as

  

Interpretation: from the graph we can observe that the line pass through $\left(40,37\right)$ and $\left(25,76\right)$ .

Using the slope formula $m=\frac{y_2-y_1}{x_2-x_1}$ we determine its value and is given as,

  $\begin{array}{l}m=\frac{76-37}{25-40}\\ =-\frac{39}{15}\end{array}$

Now to determine the y-intercept from slope intercept form equation of the line −

  $y=mx+b$ find b

Here put $y=37,x=40,m=-\frac{39}{15}$

  $\Rightarrow 37=-\frac{39}{15}\times 40+b$

  $\begin{array}{l}\therefore b=37+104\\ b=141\end{array}$

Now put the value of b in the above equation and get the desired line of equation

  $y=-\frac{39}{15}x+141$