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 regression context represents the change in the dependent variable (temperature) for a unit change in the independent variable (latitude). If the slope is negative, the dependent variable decreases as the independent variable increases. If positive, it increases.

Step2: Observe data trend

As the latitude (in degrees north) increases from 30 to 45, the high - temperature values generally decrease from 72 to 41.

Step3: Calculate approximate slope

Let $(x_1,y_1)=(30,72)$ and $(x_2,y_2)=(45,41)$. 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 calculator for linear regression. But if we do a rough estimate from the data points:
Let's take two more representative points, 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.