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:
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]
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
[tex]m=\frac{1-0}{1-0}=1[/tex]
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
[tex]m=\frac{10-1}{2-1}=\frac{9}{1}=9[/tex]
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:
[tex]m=\frac{5-1}{2-1}=\frac{4}{1}=4[/tex]
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.
