**<--That means my answer choice
1. For the data in the table does y vary directly with x? If it does write an equation for the direct variation.
x|y
8|28
16|56
20|70
a. yes;y=5x
b. yes;y=x+20
c. yes;y=3.5x**
d. no; y doesn't vary directly with x
2. For the data in the table does y vary directly with x? If it does write an equation for the direct variation.
x|y
40|32
28|16
16|12
a. no;y does not vary directly with x**
b. yes; y=2x
c. yes; y=1.5x
d. yes; y=0.2x
Please help whenever you get the chance, thank you :)
The tables are the parts that say "x,y" with the numbers under them
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To determine whether y varies directly with x, we need to check if the ratio of y to x is constant for all given data points. Let's calculate the ratio for each data point:
For the first set of data:
- For x = 8, y/x = 28/8 = 3.5
- For x = 16, y/x = 56/16 = 3.5
- For x = 20, y/x = 70/20 = 3.5
Since the ratio of y to x is constant (3.5), we can conclude that y varies directly with x. Therefore, we need to find an equation for the direct variation.
To find the equation, we can use the form y = kx, where k represents the constant ratio. Based on the data, we know that k = 3.5. So the equation for the direct variation is:
y = 3.5x
Therefore, the correct answer is c. yes; y=3.5x.
For the second set of data:
- For x = 40, y/x = 32/40 = 0.8
- For x = 28, y/x = 16/28 ≈ 0.571
- For x = 16, y/x = 12/16 = 0.75
Since the ratio of y to x is not constant, we can conclude that y does not vary directly with x. Therefore, the correct answer is a. no; y does not vary directly with x.
If you ever encounter a similar question, follow these steps:
1. Calculate the ratio of y to x for each data point.
2. If the ratio is constant for all data points, y varies directly with x. Otherwise, it doesn't.
3. Use the form y = kx to find the equation for the direct variation, where k is the constant ratio.