Question

Maria was the understudy in a Broadway show.She performed once a week. Then the lead brokeher arm. Now Maria performs 9 times a week. Whichgraph shows Maria's number of performances?101Performances수 9 오Performances+% 11% 22% 33% 44%WeeksA.+++* 1 1% 22% 33% 44%WeeksB.

Answer 1

To answer this question, we can see that:

1. We have a constant rate of change in this case since we have a linear behavior for Maria's performances per week

2. To find the rate of change for a line, we have to find the slope of the line. The slope of the line is given by:

`m=\frac{y_2-y_1_{}}{x_2-x_1}`

3. We can see that, in both graphs, we have that for the first week we have the points:

(0,0) and (1, 1)

The slope in both cases is:

(0, 0) ---> x1 = 0, y1 = 0

(1, 1) ---> x2 =1, y2 = 1

`m=(1-0)/(1-0)=1`

In we use words, we can say that Maria has one performance per week.

4. Now for the first and the second graph, we can find the slopes as follows:

Graph A

In the first week, she performs only once.

In the second week, she has a total of 10 performances.

Then we can write this in numbers as:

• (1, 1) and (2, 10)

Now we can find the slope as follows:

• (1, 1) ---> x1 = 1, y1 = 1

,

• (2, 10) ---> x2 = 2, y2 = 10

`m=(10-1)/(2-1)=(9)/(1)=9`

Therefore, for this graph, Maria performed 9 times a week.

Graph B

We can proceed similarly for this case:

In the first week, she performed only once.

In the second week, she had performed, approximately, 5 times a week.

In numbers, we can say:

• (1, 1) and (2, 5)

• (1, 1) ---> x1 = 1, y1 = 1

,

• (2, 5) ---> x2 = 2, y2 = 5

Then the slope, in this case, is:

`m=(5-1)/(2-1)=(4)/(1)=4`

According to this graph, Maria performed 4 times a week.

In summary, we can say that the graph that shows Maria's number of performances is Graph A.