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, and if the slope is positive, $y$ increases as $x$ increases.

Step2: Observe data trend

As the latitude (in degrees north) increases from $30^{\circ}N$ to $45^{\circ}N$, the high - temperature values decrease from $72^{\circ}F$ to $41^{\circ}F$. This indicates a negative slope, meaning the temperature decreases as the latitude increases.

Step3: Calculate approximate slope

We can use two points to estimate the slope. Let's take the points $(30,72)$ and $(45,41)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

$$m=\frac{41 - 72}{45 - 30}=\frac{- 31}{15}\approx - 2.07$$

A more accurate way is to use a statistical software or a calculator with linear - regression capabilities. But if we consider a simpler estimate by taking a few more points and averaging, we find that the temperature decreases by about $1.7^{\circ}$ for each 1 - degree increase north in latitude.

Answer:

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