Which table shows a proportional relationship between x and y?
x 1 3 4 7
y 2 5 8 14
x 1 2 3 4
y 4 10 12 16
x 7 14 28 35
y 1 2 4 5
x 2.5 3 5 6
y 5 6 10 15
Could someone help me with this please
Thank you!
Ah, the dreaded proportional relationship dilemma. Don't worry, I'm here to help! Let's break it down together.
The first step is to check if the y-values change at a constant rate as the x-values increase. In other words, is there a consistent pattern?
Let's look at the first table:
x 1 3 4 7
y 2 5 8 14
If we compare the y-values, we can see that they increase by 3 each time the x-value increases by 1. So, for example, when x goes from 1 to 3, y goes from 2 to 5. That means the relationship here is proportional! We have a winner!
The other tables may not have the same consistent pattern, so it seems like Table 1 shows the proportional relationship between x and y.
I hope that clears things up for you. Just remember, if in doubt, look for the pattern and embrace the humor along the way!
To determine if a table shows a proportional relationship between x and y, we need to check if the ratio of y to x is constant for all values.
Let's analyze each table:
Table 1:
x: 1 3 4 7
y: 2 5 8 14
If we calculate the ratio of y to x for each pair of values, we get:
2/1 = 2
5/3 ≈ 1.67
8/4 = 2
14/7 = 2
The ratio of y to x is not constant, so table 1 does not show a proportional relationship.
Table 2:
x: 1 2 3 4
y: 4 10 12 16
Calculating the ratio of y to x:
4/1 = 4
10/2 = 5
12/3 = 4
16/4 = 4
The ratio of y to x is not constant, so table 2 does not show a proportional relationship.
Table 3:
x: 7 14 28 35
y: 1 2 4 5
Calculating the ratio of y to x:
1/7 ≈ 0.14
2/14 ≈ 0.14
4/28 ≈ 0.14
5/35 ≈ 0.14
The ratio of y to x is constant, approximately 0.14, so table 3 does show a proportional relationship.
Table 4:
x: 2.5 3 5 6
y: 5 6 10 15
Calculating the ratio of y to x:
5/2.5 = 2
6/3 = 2
10/5 = 2
15/6 = 2.5
The ratio of y to x is not constant, so table 4 does not show a proportional relationship.
Therefore, the table that shows a proportional relationship between x and y is table 3.
To determine which table shows a proportional relationship between x and y, we need to check if the ratio between y and x is the same for each pair of values.
Let's calculate the ratio for each table:
Table 1:
x = 1, y = 2 ⟹ y/x = 2/1 = 2
x = 3, y = 5 ⟹ y/x = 5/3 ≈ 1.67
x = 4, y = 8 ⟹ y/x = 8/4 = 2
x = 7, y = 14 ⟹ y/x = 14/7 = 2
Table 2:
x = 1, y = 4 ⟹ y/x = 4/1 = 4
x = 2, y = 10 ⟹ y/x = 10/2 = 5
x = 3, y = 12 ⟹ y/x = 12/3 = 4
x = 4, y = 16 ⟹ y/x = 16/4 = 4
Table 3:
x = 7, y = 1 ⟹ y/x = 1/7 ≈ 0.143
x = 14, y = 2 ⟹ y/x = 2/14 ≈ 0.143
x = 28, y = 4 ⟹ y/x = 4/28 ≈ 0.143
x = 35, y = 5 ⟹ y/x = 5/35 ≈ 0.143
Table 4:
x = 2.5, y = 5 ⟹ y/x = 5/2.5 = 2
x = 3, y = 6 ⟹ y/x = 6/3 = 2
x = 5, y = 10 ⟹ y/x = 10/5 = 2
x = 6, y = 15 ⟹ y/x = 15/6 ≈ 2.5
From the calculations, we can see that only in Table 1 and Table 2 is the ratio of y to x always the same. Therefore, the tables that show a proportional relationship between x and y are:
Table 1:
x 1 3 4 7
y 2 5 8 14
Table 2:
x 1 2 3 4
y 4 10 12 16