Does the data in the table represent a direction variation or an inverse variation, write an equation
x 1 2 5 10
y 40 20 8 4
My answer is a direct variation, y=40x, is this correct?
here are the other answers
direct variation 7=1/40x
inverse variat xy=40
inverse xy=1/40
while 40 = 40*1, 20 ≠ 40*2
so, your first guess is wrong.
However, note that x*y=40 for all the items.
correct
the answer is C: inverse variation & xy=40
To determine whether the data in the table represents a direct variation or an inverse variation, we need to compare the ratios of corresponding values of x and y.
In a direct variation, the ratio of y to x remains constant. This means that if you divide any y-value by its corresponding x-value, you should get the same result throughout all the data points.
Let's calculate these ratios:
For the first data point:
y / x = 40 / 1 = 40
For the second data point:
y / x = 20 / 2 = 10
For the third data point:
y / x = 8 / 5 = 1.6
For the fourth data point:
y / x = 4 / 10 = 0.4
Since the ratios are not constant, the data does not represent a direct variation.
Now let's check if it represents an inverse variation. In an inverse variation, the product of the x and y values remains constant. This means that if you multiply any x-value by its corresponding y-value, the result should be the same for all the data points.
Let's calculate these products:
For the first data point:
x * y = 1 * 40 = 40
For the second data point:
x * y = 2 * 20 = 40
For the third data point:
x * y = 5 * 8 = 40
For the fourth data point:
x * y = 10 * 4 = 40
Since the products are constant, the data represents an inverse variation.
Now, to find the equation that represents inverse variation, we can use the formula xy = k, where k is the constant of variation.
Using any data point from the table (let's choose the first one: x = 1, y = 40), we can substitute these values into the equation to solve for k:
1 * 40 = k
40 = k
So the equation that represents the inverse variation in this case is xy = 40.