Determine if the tables and graphs below express a direct variation between the varia If they do, find the constant of variation and an equation that defines the relation. 1. 2. 3. 4. X y X y X y X y 1 -3 7 3 2 2 -6 1 -15 10 -20 25 -3 2 -4 5 3 4 -9 14 -21 -28 6 -9 -12 3 -12 2 4 5 3 4
Answer:
Let’s analyze each set of data to determine if they express direct variation and find the constant of variation (\(k\)) and the equation for the relation.
1. **Data Set 1 (X, Y):**
– Direct Variation: No
– Equation: Not applicable (no direct variation)
2. **Data Set 2 (X, Y):**
– Direct Variation: Yes
– Constant of Variation (\(k\)): \(3\)
– Equation: \(Y = 3X\)
3. **Data Set 3 (X, Y):**
– Direct Variation: No
– Equation: Not applicable (no direct variation)
4. **Data Set 4 (X, Y):**
– Direct Variation: Yes
– Constant of Variation (\(k\)): \(-3\)
– Equation: \(Y = -3X\)
In summary:
– Data Sets 2 and 4 express direct variation.
– The equations for these direct variations are \(Y = 3X\) and \(Y = -3X\), respectively.
– Data Sets 1 and 3 do not show direct variation.
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