Nancy wants to make a graph to show the relationship between the temperature of water, in degrees Celsius, and the time, in seconds, for which water is heated. She plots the following points:

(0, 50), (1, 60), (2, 70), (3, 80), (4, 90)

She uses the following steps to plot the graph:

- Label origin as (0, 0).
- On x-axis, label Time in minutes.
- On y-axis, label Temperature in degrees Celsius.
- The scale on x-axis starts from 0 and goes up to 5 at intervals of 1.
- The scale on the y-axis starts from 0 and goes up to 200 at intervals of 50.

Which of the following best describes the graph?

It will not be spread out horizontally across the entire coordinate plane because in Step 4, Nancy selected an incorrect scale on the axis.

It will not be spread out vertically across the entire coordinate plane because in Step 5, Nancy selected an incorrect scale on the y-axis.

It will not be spread out horizontally across the entire coordinate plane because in Step 2, Nancy plotted time instead of temperature on the axis.

It will not be spread out vertically across the entire coordinate plane because in Step 3, Nancy plotted temperature instead of time on the y-axis.

mari379
Jul 19, 2014

#5**+5 **

My view is as follows (though the question isn't really about mathematics at all - it's more about presentation!):

*Which of the following best describes the graph?*

*1. It will not be spread out horizontally across the entire coordinate plane because in Step 4, Nancy selected an incorrect scale on the axis. *This is true (though I wouldn't have used the word "incorrect") but the "incorrectness" is relatively small.

*2. It will not be spread out vertically across the entire coordinate plane because in Step 5, Nancy selected an incorrect scale on the y-axis. *This is true and the "incorrectness" is relatively large.

*3. It will not be spread out horizontally across the entire coordinate plane because in Step 2, Nancy plotted time instead of temperature on the axis. *This is plain nonsense!

*4. It will not be spread out vertically across the entire coordinate plane because in Step 3, Nancy plotted temperature instead of time on the y-axis. *This is also plain nonsense!

So, of the options on offer, I think 2. best describes the graph (but it's a really silly question!!).

Alan
Jul 22, 2014

#3**+5 **

This one is tough!!! I'm not actually sure of the answer, either, but here is my opinion:

Let's throw out the two claiming some "incorrect scale"......we can "scale" a graph in most any manner we'd like......!!!! Besides, the graph is "scaled" per the instructions....

But notice......if we chose to "scale" the temperature on the y axis by increments of 1 (like on the x axis), our graph would be extremely "vertical" ("tall").....

So, the correct answer is the last one.......choosing to scale the temperature in units of 50 keeps the vertical component "manageable."

The problem with the "answer" is that the "spread" of the graph doesn't have anything to do with what thing is being plotted on each axis......we could have plotted the temperature on the x axis, as well......it's the "scale" factor that's important.....

Do any other mathematicians have other ideas????

CPhill
Jul 21, 2014

#5**+5 **

Best Answer

My view is as follows (though the question isn't really about mathematics at all - it's more about presentation!):

*Which of the following best describes the graph?*

*1. It will not be spread out horizontally across the entire coordinate plane because in Step 4, Nancy selected an incorrect scale on the axis. *This is true (though I wouldn't have used the word "incorrect") but the "incorrectness" is relatively small.

*2. It will not be spread out vertically across the entire coordinate plane because in Step 5, Nancy selected an incorrect scale on the y-axis. *This is true and the "incorrectness" is relatively large.

*3. It will not be spread out horizontally across the entire coordinate plane because in Step 2, Nancy plotted time instead of temperature on the axis. *This is plain nonsense!

*4. It will not be spread out vertically across the entire coordinate plane because in Step 3, Nancy plotted temperature instead of time on the y-axis. *This is also plain nonsense!

So, of the options on offer, I think 2. best describes the graph (but it's a really silly question!!).

Alan
Jul 22, 2014