To determine if the relationship between the variables is a direct variation, an inverse variation, or neither, we can examine the ratio of y/x for each pair of values.
1. For X = 3, y = 15:
y/x = 15/3 = 5
2. For X = 8, y = 40:
y/x = 40/8 = 5
3. For X = 10, y = 50:
y/x = 50/10 = 5
4. For X = 22, y = 110:
y/x = 110/22 = 5
Since y/x is constant at 5 for all values, the relationship between the variables is a direct variation.
To write a function to model the direct variation, we can use the formula y = kx, where k is the constant of variation. Using any of the given data points, let's use the point (3,15):
15 = k(3)
k = 5
Therefore, the function that models the direct variation is:
y = 5x
State whether the relationship between the variables in the table is a direct variation, an inverse variation, or neither. If it is a direct or inverse variation, write a function to model it.
X: 3,8,10,22
y: 15,40,50,110
1 answer