Answers:
a) Choice D -- Graph is discrete due to b only taking on whole number values (b = 0, b = 1, b = 2, etc)
see the attached image below for the graph
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b) She bought 9 basketballs
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Explanation for part A
To make a table, we simply replace every copy of 'b' with a positive whole number. So for instance, replace b with 0 and we get
a = 18*b = 18*0 = 0
Therefore b = 0 leads to a = 0 meaning buying 0 basketballs cost the coach $0
If b = 1, then a = 18 because
a = 18*b = 18*1 = 18
So 1 basketball costs $18 as expected
2 basketballs cost a total of $36 and we see that as shown below
a = 18*b = 18*2 = 36
This pattern continues however long as you need. Each row of the table represents an ordered pair of (b,a) values. Unfortunately your teacher made 'b' the independent variable meaning that it must come first even if the temptation is to put 'a' first in the ordered pair due to alphabetical order.
To graph this function, we just plot the points from the table. Each row is an ordered pair so it represents 1 point. We do NOT connect the dots with a straight line. Why not? Because we can't buy half a basketball, so the point with b = 1/2 = 0.5 wouldn't make any sense, so it's no use to us. The fact we have disconnected points as the graph shows visually tells us that we have a discrete graph. Connecting the dots would make the graph continuous.
Once again, have a look at the image attached below for the table and graph.
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Explanation for part B
The equation in part A helps us find the pre-tax total cost. If that cost is $162, then a = 162 and b is...
a = 18*b
162 = 18*b
18*b = 162
18*b/18 = 162/18
b = 9
So she bought 9 basketballs
This is represented as point J(9,162) on the graph below.