Does the data in the table represent a direct variation or an inverse variation? x 1 3 4 7 y 5 15 20 35
A) DV; y=1/5x
B) IV; xy=5
C) DV; y=5x
D) IV; xy=1/5
looks like y=5x
so, what is that?
Steve is correct
Well, looking at the data in this table, it seems like the values of y increase as the values of x increase. It's like a roller coaster ride, the higher x goes, the higher y goes too. So, I would say it represents a direct variation. Which makes option C "DV; y=5x" the correct choice. And hey, what a coincidence, the numbers 5 and x in that option match the numbers in the table. It's almost like someone planned it that way!
To determine whether the data in the table represents a direct variation or an inverse variation, we need to check the relationship between the x and y values.
In direct variation, as x increases, y also increases, and the ratio between y and x remains constant.
In inverse variation, as x increases, y decreases, and the product of x and y remains constant.
Let's check the table:
x 1 3 4 7
y 5 15 20 35
To determine if it is a direct variation, we need to check if the ratio of y to x is constant.
For the first row, y/x = 5/1 = 5
For the second row, y/x = 15/3 = 5
For the third row, y/x = 20/4 = 5
For the fourth row, y/x = 35/7 = 5
The ratio of y to x in each row is 5, which remains constant. Therefore, the data in the table represents a direct variation.
The correct answer is C) DV; y=5x
To determine whether the data in the table represents a direct variation or an inverse variation, we need to understand the relationship between the variables x and y.
1. Direct Variation (DV): In a direct variation, the variables are directly proportional, which means that as one variable increases, the other increases as well, and vice versa. The equation that represents a direct variation is of the form y = kx, where k is a constant.
2. Inverse Variation (IV): In an inverse variation, the variables are inversely proportional, which means that as one variable increases, the other decreases, and vice versa. The equation that represents an inverse variation is of the form xy = k, where k is a constant.
Now let's examine the given data in the table:
x 1 3 4 7
y 5 15 20 35
To determine whether it's direct variation or inverse variation, we'll check if the ratios of y to x are consistent throughout the table.
For x = 1, y = 5, y/x = 5/1 = 5.
For x = 3, y = 15, y/x = 15/3 = 5.
For x = 4, y = 20, y/x = 20/4 = 5.
For x = 7, y = 35, y/x = 35/7 = 5.
Since the ratio of y to x is consistent and equal to 5 for all the values, it is evident that the data represents a direct variation.
Therefore, the correct answer is C) DV; y = 5x.