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Question

For the data in the table, tell whether y varies directly with x . If it does, write an equation for the direct variation.


x y
2 -6.6
3 -9.9
4 -13.2
5 -16.5

Answer 1

To determine whether \( y \) varies directly with \( x \), we check if the ratio \( \frac{y}{x} \) is constant for all pairs of \( (x, y) \). If it is constant, then \( y \) varies directly with \( x \), and we can express it as \( y = kx \), where \( k \) is the constant of variation.

We can calculate the ratios:

1. For \( x = 2 \) and \( y = -6.6 \): \[ \frac{y}{x} = \frac{-6.6}{2} = -3.3 \]

2. For \( x = 3 \) and \( y = -9.9 \): \[ \frac{y}{x} = \frac{-9.9}{3} = -3.3 \]

3. For \( x = 4 \) and \( y = -13.2 \): \[ \frac{y}{x} = \frac{-13.2}{4} = -3.3 \]

4. For \( x = 5 \) and \( y = -16.5 \): \[ \frac{y}{x} = \frac{-16.5}{5} = -3.3 \]

Since the ratio \( \frac{y}{x} \) is constant at \( -3.3 \) for all the pairs, we can conclude that \( y \) varies directly with \( x \).

The equation for the direct variation is: \[ y = -3.3x \]