Question

Determine the constant of proportionality for the table. Express your answer as y =kx a.X = 33y b.33k c.Y = 0.003 d.Y = 33x

Answer 1

(d)
`\( Y = 33x \)` expresses the relationship with
`\( k = 33 \)` as the constant of proportionality.

Explanation:

To determine the constant of proportionality
`(\(k\))` for the table, we need to find the relationship between the variables
`\(x\)` and
`\(y\)` and express it in the form
`\(y = kx\)`.

Without the actual table data, it's not possible to calculate the exact constant of proportionality, but I can guide you through the process. Let's assume that your table has data points
`\((x_1, y_1), (x_2, y_2), \ldots\)`.

The general formula for the constant of proportionality is
`\(k = (y)/(x)\)`. You can use any pair of corresponding values from your table to calculate
`\(k\)`.

For example, if you choose a specific pair
`\((x_1, y_1)\)`, the equation would be:

`\[k = (y_1)/(x_1)\]`

Once you have the calculated
`\(k\)`, you can express the relationship between
`\(x\)` and
`\(y\)` as
`\(y = kx\)`.

So, in terms of the given options:

(a)
`\(X = 33y\)` is not the correct form; it's expressing
`\(x\)` in terms of
`\(y\)`.

(b)
`\(33k\)` is not the correct form; it's just a constant multiplied by
`\(k\)`.

(c)
`\(Y = 0.003\)` is not the correct form; it's a constant value and doesn't represent the relationship between
`\(x\)` and
`\(y\)`.

(d)
`\(Y = 33x\)` is the correct form if
`\(k = 33\)`, as it expresses
`\(y\)` in terms of
`\(x\)`.

However, the actual value of
`\(k\)` depends on your specific data points from the table.