course Phy 201
ic-trapezoid
On a graph of income stream in dollars per month vs. clock time in months, we find the two points (16, 1000) and (40, 1200).
What do the altitudes of the graph represent?
They represent the dollars per month.
What is the rise between the two points of this graph?
200
What is the run between these points?
24
What therefore is the slope associated with this graph trapezoid?
8.3
What does the slope mean?
The slope shows that the jump from point to point is very significant, it is increasing rapidly.
The rise, the run and the slope all have units, and the slope always represents the rate of change of one quantity with respect to the other. This should have been specified in detail.
What does the base of the graph represent?
Clock time in months
What are the dimensions of the equal-area graph rectangle?
24x1,100
What is the area of the graph?
26,400
What does the area of the graph represent?
The distance from the x axis
No x axis is given in this problem.
You could specify one. Then you would probably refer to the distance moved along the x axis, rather than the distance from the x axis.
On a graph of force in pounds vs. position in feet, we find a graph rectangle with base 200 and altitude 30.
What do the altitudes of the graph represent?
force in pounds.
What is the rise between the two points of this graph?
30
What is the run between these points?
200
What therefore is the slope associated with this graph trapezoid?
.15
What does the slope mean?
It is showing a very slow change due the slow climb and the long length of the base.
I'm repeating myself here, mainly so you don't have to look back at my previous response:
The rise, the run and the slope all have units, and the slope always represents the rate of change of one quantity with respect to the other. This should have been specified in detail.
What does the base of the graph represent?
position in length.
What are the dimensions of the equal-area graph rectangle?
15x200
What is the area of the graph?
3000
What does the area of the graph represent?
On a graph of density in grams / centimeter vs. position in centimeters, we find the points (5, 12) and (20, 10).
What do the altitudes of the graph represent?
density in grams
What is the rise between the two points of this graph?
-2
What is the run between these points?
15
What therefore is the slope associated with this graph trapezoid?
-2/15
What does the slope mean?
It shows that there is a drop in position as the density is lowered.
What does the base of the graph represent?
position in centimeter.
What are the dimensions of the equal-area graph rectangle?
11x15
What is the area of the graph?
165
What does the area of the graph represent?
I'm not sure.
There's an important reasoning process here that involves the names of the quantities and their units. You're doing great with the numbers, so it shouldn't be hard to extend your understanding to the interpretation (which in some, but not all cases is pretty challenging). You first have to start using units.
See my notes.