Question

the scatterplot shows the latitudes of various united states (us) cities plotted against the city’s average september temperature, where ( l ) is the latitude of the city, in degrees, and ( t ) is the city’s average september temperature, in degrees fahrenheit (( ^circ f )). a line that approximates the data is shown on the graph. which of the following statements is the best interpretation for the slope of the line of best fit in this situation? choose 1 answer: a) the average september temperature for a us city decreases by ( 2^circ f ) for each 3 degree increase in latitude. b) the average september temperature for a us city increases by ( 2^circ f ) for each 3 degree increase in latitude. c) the average september temperature for a us city decreases by ( 3^circ f ) for each 2 degree increase in latitude. d) the average september temperature for a us city increases by ( 3^circ f ) for each 2 degree increase in latitude.

Explanation:

Step1: Analyze the trend of the line

The line of best fit in the scatterplot has a negative slope (it's decreasing from left to right), which means as latitude (\(l\)) increases, temperature (\(T\)) decreases. So we can eliminate options B and D which suggest an increase in temperature with increasing latitude.

Step2: Determine the slope interpretation

To find the slope, we look at the change in \(T\) (temperature) over the change in \(l\) (latitude). From the graph, we can see that as latitude increases (moves to the right), temperature decreases (moves down). Let's consider the direction of change. For a line with negative slope, the change in \(T\) is negative when change in \(l\) is positive. Now, looking at the options A and C:

• Option A: Decrease of \(2^\circ F\) for each \(3\) degree increase in latitude. So the slope would be \(\frac{\Delta T}{\Delta l}=\frac{- 2}{3}\) (negative, which matches the decreasing line).
• Option C: Decrease of \(3^\circ F\) for each \(2\) degree increase in latitude. Slope would be \(\frac{-3}{2}\), but visually, the rate of decrease (how much \(T\) drops per \(l\) increase) seems to match a smaller magnitude of slope (like \(\frac{-2}{3}\) rather than \(\frac{-3}{2}\)) when we look at the scatterplot's line. Also, the key is the direction (decrease) and the ratio. Since the line is decreasing, and the ratio of temperature decrease to latitude increase is \(2\) to \(3\) (as in option A), that's the correct interpretation.

Answer:

A. The average September temperature for a US city decreases by \(2^\circ F\) for each \(3\) degree increase in latitude.