Question

the scatter plot below shows the relationship between latitude of cities and their average january temperature. which of the following is the best estimate of the average change in temperature associated with a 1° increase in latitude? choose 1 answer: a -15°f b -2.5°f c 2.5°f d 15°f

Explanation:

Step1: Recall slope concept

The average change in temperature associated with a $1^{\circ}$ increase in latitude is the slope of the line - of - best - fit for the scatter - plot. If the relationship is approximately linear, we can estimate the slope using two points on the line of best - fit.

Step2: Assume two points

Let's assume two points on the line of best - fit. As latitude increases, temperature generally decreases, so the slope will be negative. A reasonable estimate is that if we consider a change in latitude of say 6 degrees (for example, from 30 degrees latitude to 36 degrees latitude) and a corresponding change in temperature of about 15 degrees Fahrenheit decrease.

Step3: Calculate slope

The slope $m=\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in temperature and $\Delta x$ is the change in latitude. If $\Delta x = 6$ and $\Delta y=- 15$, then $m=\frac{-15}{6}=-2.5$. So the average change in temperature associated with a $1^{\circ}$ increase in latitude is approximately $-2.5^{\circ}F$.

Answer:

B. $-2.5^{\circ}F$