Determine if the tables and graphs below express a direct variation between the variables. If they do, find the constant of variation and
Answer:
1. Yes, the variables \(x\) and \(y\) have a direct variation. The constant of variation is -3. The equation that defines the relation is \(y = -3x\).
2. No, the variables \(x\) and \(y\) do not have a direct variation.
3. No, the variables \(x\) and \(y\) do not have a direct variation.
4. Yes, the variables \(x\) and \(y\) have a direct variation. The constant of variation is 1. The equation that defines the relation is \(y = x\).
5. Yes, the variables \(x\) and \(y\) have a direct variation. The constant of variation is \(\frac{3}{4}\). The equation that defines the relation is \(y = \frac{3}{4}x\).
Step-by-step explanation:
1. The variables \(x\) and \(y\) have a direct variation. The equation is \(y = -3x\).
2. The variables \(x\) and \(y\) do not have a direct variation.
3. The variables \(x\) and \(y\) do not have a direct variation.
4. The variables \(x\) and \(y\) have a direct variation. The equation is \(y = x\).
5. The variables \(x\) and \(y\) have a direct variation. The equation is \(y = \frac{3}{4}x\).
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