To determine the missing value in a proportional relationship, we can use the concept of ratios. In a proportional relationship, the ratio of corresponding values of \(x\) and \(y\) remains constant.
From the provided pairs:
- \((-3, 9)\)
- \((-5, ?)\)
- \((-7, 21)\)
- \((-18, -15)\)
- \((15, 18)\)
First, we calculate the ratios for known pairs:
-
For \((-3, 9)\): \[ \frac{y}{x} = \frac{9}{-3} = -3 \]
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For \((-7, 21)\): \[ \frac{y}{x} = \frac{21}{-7} = -3 \]
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For \((-18, -15)\): \[ \frac{y}{x} = \frac{-15}{-18} = \frac{5}{6} \]
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For \((15, 18)\): \[ \frac{y}{x} = \frac{18}{15} = \frac{6}{5} \]
It looks like the pairs \((-3, 9)\) and \((-7, 21)\) confirm a constant ratio of \(-3\). Now we can find the missing \(y\) value for \(x = -5\) by using the ratio of \(-3\):
Setting up the equation based on the ratio: \[ \frac{y}{-5} = -3 \] Multiplying both sides by \(-5\): \[ y = -3 \times -5 = 15 \]
Thus, the missing value for \(y\) when \(x = -5\) is \(15\).
Final answer: 15