2 floors/second
Step-by-step explanation:
The points on the graph at the ends of the interval of interest are ...
(seconds, floors) = (3, 3) and (5, 7)
The slope of the line between these points is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
where the points are (x1, y1) and (x2, y2). For the points shown above, the slope is ...
m = (7 floors -3 floors)/(5 seconds -3 seconds)
= (4 floors)/(2 seconds) = 4/2 floors/second = 2 floors/second
In your answer form:
A = 2
B = floors
C = second
Additional comment
Any measurement will vary, depending on the units in which the measurement is made. A length, for example, might be 12 inches, or 1 foot. The length numbers 12 or 1 don't mean anything, unless you know the units they are counting.
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When x- and y-values are pure numbers, their ratio, or the ratio of their changes, is a pure number. It has no units. We do a lot of algebra this way. (This is mainly to get you used to doing the arithmetic without having the confusion of units getting in the way.)
When x- and y-values on a graph are identified as having particular units, the slope of any curve on that graph has units that are the ratio of the y-units to the x-units. (Any area on the graph will be the product of the x-units and the y-units.)
Here, the units of the vertical (y) scale are "floors." The units of the horizontal (x) scale are "seconds". You know this because that is how the graph is labeled. Then the slope of a line on the graph has units of ...
"y-units"/"x-units" = floors/second
The choice of singular or plural for the units depends a little on what makes sense in English. Usually, the denominator unit will be singular. Often, the numerator unit is plural, especially of the value is more than 1.
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As we show above, you can do the math with the units attached to the numbers. They are treated algebraically as though they are variables. Only numbers with like units can be added or subtracted. (You cannot add (combine) 3 inches and 4 feet for the same reason you cannot add 3x and 4y—they are unlike terms.) You can multiply and divide units as needed. For computing area, we often do something like (3 ft)(4 ft) = 12 ft·ft = 12 ft².
If you make it a practice to consider units along with the numbers, you will find they help you do the correct arithmetic. If you are considering an area computation that does not result in square units, for example, you might need to do a units conversion or reconsider the proposed computation. Using units in computation is especially helpful in physics and chemistry.
