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