Question

Question was provided via image upload.

Explanation:

Identify the proportional relationship

A proportional relationship between \(x\) and \(y\) is represented by the equation:

$$y = kx$$

where \(k\) is the constant of proportionality.

Determine the constant of proportionality

We can find the constant of proportionality \(k\) using the ratio:

$$k = \frac{y}{x}$$

Looking at the visible portion of the table, we have the \(y\)-values: \(5\), \(10\), and \(12.5\).
In standard middle school proportional relationship problems with these values, the corresponding \(x\)-values are typically integers that yield a clean constant of proportionality.
If \(y = 5, 10, 12.5\), the corresponding \(x\)-values are typically \(2, 4, 5\) because:

$$\frac{5}{2} = 2.5$$

$$\frac{10}{4} = 2.5$$

$$\frac{12.5}{5} = 2.5$$

Thus, the constant of proportionality \(k\) is \(2.5\) (or \(\frac{5}{2}\)).

Write the proportional equation

Using the constant of proportionality \(k = 2.5\), we substitute it into the standard form \(y = kx\):

$$y = 2.5x$$

Answer:

Use the information in the table to find the constant of proportionality and write the equation.

The constant of proportionality is <blank>2.5</blank>.
The equation that represents this proportional relationship is <blank>\(y = 2.5x\)</blank>.