Math worksheet on finding the constant of proportionality with answer key.

I'll solve this problem step by step. The task is to find the constant of proportionality for each table and then color the corresponding problem number based on the answer key provided at the bottom.

Let me analyze each table one by one:

Table 1:
X: 2, 4, 6, 8, 10
Y: 5, 10, 15, 20, 25
The constant of proportionality is Y/X = 5/2 = 2.5

Table 2:
X: 2, 4, 6, 8, 10
Y: 8, 4, 0, -4, -8
This is not proportional since Y/X is not constant (8/2=4, 4/4=1, 0/6=0, etc.)

Table 3:
X: 2, 1, -1, -2, -3
Y: 6, 3, -3, -6, -9
The constant of proportionality is Y/X = 6/2 = 3

Table 4:
X: 3, 4, 5, 6, 7
Y: 6, 8, 10, 12, 14
The constant of proportionality is Y/X = 6/3 = 2

Table 5:
X: 15, 18, 21, 24, 27
Y: 25, 30, 35, 40, 45
The constant of proportionality is Y/X = 25/15 = 5/3 ≈ 1.67

Table 6:
X: 4, 6, 12, 20, 24
Y: 7, -34, -21, -28, -42
This is not proportional since Y/X is not constant.

Table 7:
X: 54, -52, -59, 6, 4
Y: 27, -26, -29.5, 3, 2
The constant of proportionality is Y/X = 27/54 = 0.5

Table 8:
X: 0, 1, 2, 4, 7
Y: 0, 1, 2, 4, 7
The constant of proportionality is Y/X = 1/1 = 1 (for non-zero X values)

Table 9:
X: 3, -6, -12, -18, -24
Y: 2, -4, -8, -12, -16
The constant of proportionality is Y/X = 2/3 ≈ 0.67

Table 10:
X: 7, 10, 20, 11, 15
Y: 28, 40, 80, 44, 60
The constant of proportionality is Y/X = 28/7 = 4

Now I need to match these answers with the color key:
- Red: 2
- Orange: 3
- Green: 2.5
- Brown: 1.67 (5/3)
- Blue: 0.5
- Purple: 1
- Black: 0.67 (2/3)
- Pink: 4

Based on my calculations:
- Table 1: 2.5 → Green
- Table 2: Not proportional → No color (or perhaps needs to be marked as such)
- Table 3: 3 → Orange
- Table 4: 2 → Red
- Table 5: 1.67 → Brown
- Table 6: Not proportional → No color
- Table 7: 0.5 → Blue
- Table 8: 1 → Purple
- Table 9: 0.67 → Black
- Table 10: 4 → Pink

I should double-check my work, especially for tables that might not be proportional or where I might have made calculation errors.

Let me verify Table 2 again:
X: 2, 4, 6, 8, 10
Y: 8, 4, 0, -4, -8
Y/X: 4, 1, 0, -0.5, -0.8 - definitely not proportional.

Table 6:
X: 4, 6, 12, 20, 24
Y: 7, -34, -21, -28, -42
Y/X: 1.75, -5.67, -1.75, -1.4, -1.75 - not proportional.

My analysis seems correct. The final coloring would be:
1: Green
2: Not proportional (no color or special marking)
3: Orange
4: Red
5: Brown
6: Not proportional (no color or special marking)
7: Blue
8: Purple
9: Black
10: Pink