More Proportional Relationship Representations Quick Check
2 of 52 of 5 Items
Question
Use the table to answer the question.
X Y Z
1 3 18
2 6 36
3 9 54
Which option correctly uses the proportionality symbol to represent all the proportional relationships shown in the table?
(1 point)
Responses
Z∝Y and Y∝X and Z∝X
upper Z proportional to upper Y and upper Y proportional to upper X and upper Z proportional to upper X
Y∝Z and X∝Y and X∝Z
upper Y proportional to upper Z and upper X proportional to upper Y and upper X proportional to upper Z
Z∝Y and Y∝X
upper Z proportional to upper Y and upper Y proportional to upper X
18∝3 and 3∝1 and 18∝1
upper Z proportional to upper Y and upper Y proportional to upper X
More Proportional Relationship Representations Quick Check
3 of 53 of 5 Items
Question
Use the image to answer the question.
A coordinate plane shows a line connecting three data points. Both the axes range from negative 20 to 20 in increments of 5. The coordinates are left parenthesis 1 comma 5 right parenthesis, left parenthesis 2 comma 10 right parenthesis, and left parenthesis 3 comma 15 right parenthesis.
What is the constant of proportionality for the proportional relationship represented in the graph?
(1 point)
Responses
5
5
153=102=51
Start Fraction 15 over 3 End Fraction equals Start Fraction 10 over 2 End Fraction equals Start Fraction 5 over 1 End Fraction
0.2
0.2
153
Start Fraction 15 over 3 End Fraction equals Start Fraction 10 over 2 End Fraction equals Start Fraction 5 over 1 End Fraction
To determine the correct option that uses the proportionality symbol to represent the proportional relationships shown in the table, we need to analyze the relationships between the variables X, Y, and Z.
Looking at the values in the table, we can see that Z is directly proportional to both Y and X. This means that as Y and X increase, Z also increases at a constant rate. Therefore, the correct option would include Z∝Y and Z∝X.
Next, let's consider the relationship between Y and X. We can observe that Y is also directly proportional to X. As X increases, Y also increases at a constant rate. Therefore, the correct option would also include Y∝X.
Now, putting it all together, we can conclude that the option that correctly uses the proportionality symbol to represent all the proportional relationships in the table is:
Z∝Y and Y∝X and Z∝X