Kevin is told that for a particular math problem, the value of y

Question

𝑦
is always 32 times the value of x
𝑥
. Kevin writes the equation y=32x
𝑦
=
32
𝑥
to show the relationship between x
𝑥
and y
𝑦
. What is the constant of proportionality?(1 point)

Answer 1

In the equation \( y = 32x \), the constant of proportionality is the coefficient of \( x \). In this case, it is 32. Thus, the constant of proportionality is \( 32 \).

Answer 2

Kevin is told that for a particular math problem, the value of y is always 32 times the value of x Kevin writes the equation y=32xto show the relationship between x and y What is the constant of proportionality?(1 point)

Answer 3

In the equation \( y = 32x \), the constant of proportionality is the coefficient of \( x \). In this case, it is \( 32 \). Therefore, the constant of proportionality is \( 32 \).

Answer 4

If a graph is proportional, what characteristic does it display?(1 point)
Responses

It will curve.
It will curve.

It will have y
𝑦
-values larger than their corresponding x
𝑥
-values.
It will have y -values larger than their corresponding x -values.

It will pass through the point (0, 0)

It will pass through the point Left Parenthesis 0 comma 0 Right Parenthesis .

It will climb rapidly, indicating a steep slope.

Answer 5

If a graph is proportional, the characteristic it displays is:

It will pass through the point (0, 0).

This indicates that as \( x \) increases, \( y \) increases proportionately, and when \( x = 0 \), \( y \) is also \( 0 \).

Answer 6

Identify the table that demonstrates a proportional relationship.(1 point)
Responses

x y
4 2
9 3
16 4

x y
10 2
15 3
40 8




x y
2 10
5 20
6 30

x y
8 2
12 3
40 4

Answer 7

To determine which table demonstrates a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for each \( x, y \) pair within the tables.

1. Table 1:

   • \( \frac{2}{4} = 0.5 \)
   • \( \frac{3}{9} \approx 0.33 \)
   • \( \frac{4}{16} = 0.25 \)
   • Not proportional.

2. Table 2:

   • \( \frac{2}{10} = 0.2 \)
   • \( \frac{3}{15} = 0.2 \)
   • \( \frac{8}{40} = 0.2 \)
   • Constant ratio of 0.2. Proportional.

3. Table 3:

   • \( \frac{10}{2} = 5 \)
   • \( \frac{20}{5} = 4 \)
   • \( \frac{30}{6} = 5 \)
   • Not proportional.

4. Table 4:

   • \( \frac{2}{8} = 0.25 \)
   • \( \frac{3}{12} = 0.25 \)
   • \( \frac{4}{40} = 0.1 \)
   • Not proportional.

From this analysis, the table that demonstrates a proportional relationship is:

Table 2.

Answer 8

# of Trees # of Apples
2 26
3 39
6 78
10 130
12 156
Determine if the quantities in the data table are in a proportional relationship. If they are not in a proportional relationship, indicate why.

(1 point)
Responses

No, the table does not count consecutively.
No, the table does not count consecutively.

Yes, the data table has a proportional relationship.
Yes, the data table has a proportional relationship.

No, the ratios are not equivalent.
No, the ratios are not equivalent.

No, the ratio 6:78
6
:
78
is not proportional to the other ratio

Answer 9

To determine if the quantities in the data table are in a proportional relationship, we need to assess if the ratio \( \frac{\text{# of Apples}}{\text{# of Trees}} \) remains constant across all entries.

Let's calculate the ratios for the data provided:

1. For 2 trees and 26 apples:
   \( \frac{26}{2} = 13 \)

2. For 3 trees and 39 apples:
   \( \frac{39}{3} = 13 \)

3. For 6 trees and 78 apples:
   \( \frac{78}{6} = 13 \)

4. For 10 trees and 130 apples:
   \( \frac{130}{10} = 13 \)

5. For 12 trees and 156 apples:
   \( \frac{156}{12} = 13 \)

Since all the calculated ratios are equal to 13, the quantities in the data table are in a proportional relationship.

Thus, the correct response is:

Yes, the data table has a proportional relationship.