Chapter 8.6, Problem 25STP

To determine

To find: the slope of the line that fits these data?

Answer to Problem 25STP

The correct option is C.

Explanation of Solution

Given:

Degrees Fahrenheit	Degree Celsius
5	-15
14	-10
41	5
77	25

  $-\frac{9}{5}$

  $-\frac{5}{9}$

  $\frac{5}{9}$

  $\frac{9}{5}$

Calculation:

Consider the table that shows number of degrees Celsius for certain Fahrenheit temperatures:

Degrees Fahrenheit ( x )	Degree Celsius ( y )
5	-15
14	-10
41	5
77	25

Slope of the line (m) passing through two points is ratio of the difference in y-coordinates tothe corresponding difference in x- coordinates.

So, if two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ then slope is:

  $m=\frac{y_2-y_1}{x_2-x_1}$

Consider that $\left(x_1,y_1\right)=\left(5,-15\right)\text{ and }\left(x_2,y_2\right)=\left(14,-10\right)$

Put the value in slope formula:

  $\begin{array}{l}m=\frac{-10-\left(-15\right)}{14-5}\\ =\frac{-10+15}{9}\\ =\frac{5}{9}\end{array}$

Therefore, the correct option is C.

Conclusion:

Therefore, the correct option is C.