To determine whether the relation in the table represents direct variation, inverse variation, or neither, we need to analyze the relationship between the x-values and y-values.
For direct variation, the ratio of y to x should be constant. Let's calculate the ratio for each set of points:
- For x = 5, y = 2, y/x = 2/5
- For x = 10, y = 1, y/x = 1/10
- For x = 15, y = 2/3, y/x = 2/3 / 15 = 2/45
- For x = 20, y = 1/2, y/x = 1/2 / 20 = 1/40
Since the ratios are not constant, the relation does not represent direct variation.
For inverse variation, the product of x and y should be constant. Let's calculate the product for each set of points:
- For x = 5, y = 2, xy = 5 * 2 = 10
- For x = 10, y = 1, xy = 10 * 1 = 10
- For x = 15, y = 2/3, xy = 15 * 2/3 = 10
- For x = 20, y = 1/2, xy = 20 * 1/2 = 10
Since the product of x and y is constant for all the data points, the relation in the table represents inverse variation.
Therefore, the equation representing the relation is:
x * y = k
Where k is the constant value of the product of x and y. In this case, k = 10.
The equation can be simplified to:
xy = 10
So, the relation in the table represents inverse variation, and the equation representing the relation is xy = 10.
Essay
Note: Your teacher will review your response to ensure you receive proper credit for your answer.
Does the relation in the table represent direct variation, inverse variation, or neither? If it is direct or inverse variation, write an equation to represent the relation. Explain your answer.
x 5 10 15 20
y 2 1 StartFraction 2 over 3 EndFraction StartFraction 1 over 2 EndFraction(3 points)
1 answer