Does the data in the table represent a direct variation or an inverse variation?
x 1 3 4 7
y 5 15 20 35
Write an equation to model the data in the table
y=5x
To determine whether the data in the table represents a direct variation or an inverse variation, we need to check if there is a constant ratio between the x-values and the y-values.
Step 1: Check for Direct Variation
In direct variation, the ratio between the x-values and y-values remains constant.
Let's calculate the ratios for the given data:
1/5 = 0.2
3/15 = 0.2
4/20 = 0.2
7/35 = 0.2
Since the ratios are equal (0.2) for all the values, we can conclude that the data represents a direct variation.
Step 2: Write an Equation to Model the Data
In a direct variation, the equation takes the form y = kx, where k is the constant of variation.
To find the value of k, we can pick any single pair of x and y values from the table. Let's use x = 1 and y = 5 for simplicity:
5 = k * 1
Solving for k:
k = 5/1
k = 5
Therefore, the equation to model the data in the table is y = 5x, since the constant of variation is 5.