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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
3 mc012-2.jpg
4 mc012-3.jpg
5 mc012-4.jpg





no

yes;

yes; y = x – 3.3

yes; y = –3.3x

1 answer

To determine if \( y \) varies directly with \( x \), we need to check if the ratio \( \frac{y}{x} \) is constant for all values of \( x \).

  1. Given the table of values, we extract the values:
    • When \( x = 2 \), \( y = \) ?
    • When \( x = 3 \), \( y = \) ?
    • When \( x = 4 \), \( y = \) ?
    • When \( x = 5 \), \( y = \) ?

However, the specific \( y \) values are not provided in the table you've shared.

If we had specific \( y \) values for each corresponding \( x \), we would calculate:

  • \( k = \frac{y}{x} \) for each pair of \( (x, y) \)
  • If \( k \) is the same across all pairs, then \( y \) varies directly with \( x \), and the equation will be of the form \( y = kx \).

If you can provide the specific \( y \) values corresponding to each \( x \), I'd be happy to help you further determine if \( y \) varies directly with \( x \) and formulate the equation!