To which subset of real numbers does -3 belong?
a) integers
b) irrational numbers
c) integers and rational numbers
d) whole numbers, integers, and rational numbers

Explanation:

The set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...} basically any number that does not have a decimal or fractional part to it. We can say that this set is composed of positive and negative whole numbers along with 0. So this is why -3 is in the set of integers.

The value -3 is not in the set of whole numbers because the set of whole numbers is {0, 1, 2, 3, 4, 5, 6, ...}, so this rules out choice D.

Choice B is also eliminated because -3 is a rational number. We can write -3 as a fraction of two integers, example: -3 = -3/1. Any rational number is not irrational, and vice versa.

Choice A is ruled out because it's not the most complete answer (though its technically true).

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."