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In a direct variation, when . Write a direct variation equation that shows the relationship between and .Write your answer as an equation with first, followed by an equals sign.
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Q. In a direct variation, when . Write a direct variation equation that shows the relationship between and .Write your answer as an equation with first, followed by an equals sign.
- Definition of direct variation: Direct variation means that `y` varies directly with `x,` which can be expressed as `y =` kx, where `k` is the constant of variation.
- Finding the constant of variation: To find the constant of variation `(k),` we can use the given values of `x` and `y`. We know that `y = 6` when `x = 2,` so we can substitute these values into the direct variation equation `y =` kx to solve for k.
- Substituting values into the equation: Substituting the given values into the equation gives us `6 = k *` 2.
- Solving for `k:` To solve for `k,` we divide both sides of the equation by `2,` which gives us `k = 6 /` 2.
- Calculating the division: Calculating the division gives us `k =` 3.
- Writing the direct variation equation: Now that we have the constant of variation, we can write the direct variation equation as `y = 3x.
