For the data in the table, does š‘¦ vary directly with š‘„? If it does, write an equation for the direct variation.

1 answer

To determine whether š‘¦ varies directly with š‘„, we need to check if the ratio š‘¦/š‘„ remains constant for all the given values.

Let's calculate the ratio for each pair of š‘„ and š‘¦:

For the first pair, š‘¦/š‘„ = 4/0.5 = 8
For the second pair, š‘¦/š‘„ = 6/0.75 = 8
For the third pair, š‘¦/š‘„ = 8/1 = 8
For the fourth pair, š‘¦/š‘„ = 10/1.25 = 8

Since the ratio š‘¦/š‘„ is constant (equal to 8) for all the values, we can conclude that š‘¦ does vary directly with š‘„.

The equation for direct variation can be written as:

š‘¦ = kš‘„

To find the value of k, we can use any pair of š‘„ and š‘¦ from the table. Let's use the first pair (0.5, 4):

4 = k * 0.5

To isolate k, we divide both sides by 0.5:

k = 4 / 0.5
k = 8

Therefore, the equation for direct variation is:

š‘¦ = 8š‘„