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A table displays a relationship between the number of mules and the bales of hay.

The left column, titled "# of Mules", lists the following values: 2, 4, 6, 8, and 10.

The right column, titled "Bales of Hay", lists the corresponding values: 1, 2, 3, 4, and 5.

Each row represents a pair of data points which indicate a proportional relationship. For every 2 mules, there is 1 bale of hay. For every 4 mules, there are 2 bales of hay, and so on.

Which equation matches this table?

Responses

y = x + 2
y = x + 2

y = -1/2 x
y = -1/2 x

y = 1/2 x + 2
y = 1/2 x + 2

y = 1/2 x
y = 1/2 x

y = -2x + 1
y = -2x + 1

y = 2x

1 answer

To find the equation that matches the relationship displayed in the table, we first note that the number of bales of hay is proportional to the number of mules.

From the data provided:

  • For every 2 mules, there is 1 bale of hay.

This indicates that the relationship can be expressed as: \[ \text{Bales of Hay} = \frac{1}{2} \times \text{# of Mules} \]

Thus we can represent this equation as: \[ y = \frac{1}{2} x \] where \(y\) represents the number of bales of hay and \(x\) represents the number of mules.

Given the options:

  1. \(y = x + 2\)
  2. \(y = -\frac{1}{2} x\)
  3. \(y = \frac{1}{2} x + 2\)
  4. \(y = \frac{1}{2} x\)
  5. \(y = -2x + 1\)
  6. \(y = 2x\)

The correct equation that matches the relationship in the table is: \(y = \frac{1}{2} x\).