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. temperature vs. latitude

latitude (°n)	42	45	39	35	32	41	40	33	30
high temp. (°f)	53	41	67	63	70	58	61	67	72	which statement describes the slope of the line of best fit for the data? the temperature decreases by about 0.9° 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 increases by about 0.8° for each 1 degree increase north in latitude. the temperature increases by about 1.3° for each 1 degree increase north in latitude.

Explanation:

Step1: Recall slope concept

The slope of the line of best - fit in a scatter - plot of latitude (independent variable $x$) and temperature (dependent variable $y$) represents the change in $y$ for a unit change in $x$. If the slope is negative, $y$ decreases as $x$ increases; if positive, $y$ increases as $x$ increases.

Step2: Observe data trend

As the latitude (in degrees north) increases from $30$ to $45$, the high temperature decreases from $72^{\circ}F$ to $41^{\circ}F$.

Step3: Calculate approximate slope

The change in latitude $\Delta x=45 - 30=15$ degrees. The change in temperature $\Delta y=41 - 72=- 31$ degrees. The slope $m=\frac{\Delta y}{\Delta x}=\frac{-31}{15}\approx - 2.07$. But we can also use a more pairwise comparison. For example, when latitude changes from $32$ to $42$ (a change of $\Delta x = 10$ degrees), temperature changes from $70$ to $53$ (a change of $\Delta y=53 - 70=-17$ degrees). Then $m=\frac{\Delta y}{\Delta x}=\frac{-17}{10}=-1.7$.

Answer:

The temperature decreases by about $1.7^{\circ}$ for each 1 degree increase north in latitude.