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Patterns and Linear Functions
Multiple Choice
Use the diagram below for questions 1–2.
A diagram labeled '1 rectangle' is on the left with a height of 8 and a width of 5. In the middle, above the label '2 rectangles,' 2 rectangles of the same dimensions are attached along their longer sides, making one larger rectangle. To the right, '3 rectangles' shows 3 rectangles attached along their longer sides making a single larger rectangle.
1. Which of the following tables represents the relationship in the diagram above? (1 point)
Number of Rectangles Perimeter
1
52
2
72
3
92
Number of Rectangles Perimeter
1
13
2
18
3
23
Number of Rectangles Perimeter
1
26
2
36
3
46
Number of Rectangles Perimeter
1
26
2
44
3
62
2. Which of the following graphs represents the relationship in the diagram? (1 point)
3.2aThe x-axis is labeled rectangles and has numbers from 2 to 4 with a step size of 2. The y-axis is labeled perimeter and has numbers from 0 to 120 with a step size of 30. The scatter plot shows these approximate points: left-parenthesis 1 comma 15 right-parenthesis, left-parenthesis 2 comma 15 right-parenthesis, left-parenthesis 4 comma 25 right-parenthesis, left-parenthesis 4 comma 30 right-parenthesis, left-parenthesis 5 comma 35 right-parenthesis
3.2bThe x-axis is labeled rectangles and has numbers from 2 to 4 with a step size of 2. The y-axis is labeled perimeter and has numbers from 0 to 120 with a step size of 30. The scatter plot shows these approximate points: left-parenthesis 1 comma 25 right-parenthesis, left-parenthesis 2 comma 40 right-parenthesis, left-parenthesis 3 comma 45 right-parenthesis, left-parenthesis 4 comma 55 right-parenthesis, left-parenthesis 5 comma 70 right-parenthesis.
3.2crThe x-axis is labeled rectangles and has numbers from 2 to 4 with a step size of 2. The y-axis is labeled perimeter and has numbers from 0 to 120 with a step size of 30. The scatter plot shows these approximate points: left-parenthesis 1 comma 50 right-parenthesis, left-parenthesis 2 comma 75 right-parenthesis, left-parenthesis 3 comma 95 right-parenthesis, left-parenthesis 4 comma 110 right-parenthesis, left-parenthesis 5 comma 135 right-parenthesis.
3.2drThe x-axis is labeled rectangles and has numbers from 2 to 4 with a step size of 2. The y-axis is labeled perimeter and has numbers from 0 to 120 with a step size of 30. The scatter plot shows these approximate points: left-parenthesis 1 comma 25 right-parenthesis, left-parenthesis 2 comma 45 right-parenthesis, left-parenthesis 3 comma 65 right-parenthesis, left-parenthesis 4 comma 80 right-parenthesis, left-parenthesis 5 comma 100 right-parenthesis.
Use the table for questions 3–4.
The table below shows the relationship between the number of sports teams to which a person belongs and the amount of free time the person has per week.
Number of Sports Teams Free Time (hours)
0
46
1
39
2
32
3
25
3. Is the above relationship a linear function? (1 point)
yes
no
4. What is the graph for the above relationship? (1 point)
graph aThe Sports team is on the x axis and the free time is on the y axis. The first sports team has 7 hours of free time. The second sports team has 15 hours of free time. The third sports team has 21 hours of free time. The fourth sports team has 29 hours of free time. The fifth sports team has 35 hours of free time.
graph bThe free time is on the y axis and the number of sports team is on the x axis. The first sports team has 39 hours of free time. The second sports team has 33 hours of free time. The third sports team has 25 hours of free time. The fourth sports team has 19 hours of free time. The fifth sports team has 11 hours of free time.
graph cThe first sports team has 18 hours of free time. The second sports team has 25 hours of free time. The third sports team has 33 hours of free time. The fourth sports team has 40 hours of free time and the fifth sports team has 46 hours of free time.
graph d
wowthat'salotofstuffpostedthatyouexpectsomeonetodoforyouwithnoeffortonyourpartthatandthetotallackofpunctuationcoupledwiththeannoyingverbiageusedinsteadofjustypingfrtactionslikerealmathprettymuchguaranteesthatnoonewilltry toevenfigureoutjustwhatit'sallabout.
I apologize, but I cannot see the graphs or tables you have mentioned. Could you please describe them to me in words so that I can assist you?
The correct answers are:
1. The correct table that represents the relationship in the diagram is:\
Number of Rectangles Perimeter\
1 92\
2 72\
3 52
2. The correct graph that represents the relationship in the diagram is:\
3.2b
To answer question 1, we need to determine the relationship between the number of rectangles and the perimeter. Looking at the diagram, we can see that each new rectangle added increases the perimeter by a fixed amount. In this case, each additional rectangle increases the perimeter by 20.
So, the correct table is:
Number of Rectangles Perimeter
1 52
2 72
3 92
To answer question 2, we need to determine the graph that represents the relationship between the number of rectangles and the perimeter. Looking at the diagram, we can see that as the number of rectangles increases, the perimeter also increases. Therefore, we need to find a graph that shows a positive linear relationship.
The correct graph is graph (b):
The x-axis represents the number of rectangles, and the y-axis represents the perimeter. The points on the graph show the approximate perimeter values for each corresponding number of rectangles.
To answer question 3, we need to determine if the relationship between the number of sports teams and free time is a linear function. A linear function is a function where the change in the dependent variable (free time) is constant for every unit change in the independent variable (number of sports teams).
Looking at the table, we can see that as the number of sports teams increases, the free time decreases, but the decrease is not constant. Therefore, the relationship is not a linear function.
To answer question 4, we need to identify the graph that represents the relationship between the number of sports teams and free time.
The correct graph is graph (b):
The x-axis represents the number of sports teams, and the y-axis represents the free time. The points on the graph show the approximate free time values for each corresponding number of sports teams.