Question

latitude and longitude describe locations on the earth with respect to the equator and prime meridian. the table shows the latitude and daily high temperatures on the first day of spring for different locations with the same longitude. which statement describes the slope of the line of best fit for the data? the temperature increases by about 1.3° for each 1 degree increase north in latitude. the temperature increases by about 0.8° for each 1 degree increase north in latitude. the temperature decreases by about 1.7° for each 1 degree increase north in latitude. the temperature decreases by about 0.9° for each 1 degree increase north in latitude.

Explanation:

Step1: Recall slope - calculation formula

The slope formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let latitude be \(x\) (independent variable) and temperature be \(y\) (dependent variable).

Step2: Select two points

Let's take \((x_1,y_1)=(30,72)\) and \((x_2,y_2)=(45,41)\).

Step3: Calculate the slope

\[m=\frac{41 - 72}{45 - 30}=\frac{- 31}{15}\approx - 2.07\]
Let's take another pair, say \((x_1,y_1)=(32,70)\) and \((x_2,y_2)=(42,53)\)
\[m=\frac{53 - 70}{42 - 32}=\frac{-17}{10}=-1.7\]

Answer:

The temperature decreases by about 1.7° for each 1 - degree increase north in latitude.