https://file.aiquickdraw.com/mathbot/file/1729170686396gsdkmany.jpg

To determine which table represents a **proportional relationship** between \(x\) and \(y\), we must check if the ratio \(\frac{y}{x}\) remains constant for each pair of values in the table. 

Let's analyze the tables:

### First Table:
\[
\begin{array}{c|c}
x & y \\
\hline
-2 & -4 \\
-1 & -2 \\
0  & 0  \\
2  & 0  \\
\end{array}
\]
Checking the ratio \(\frac{y}{x}\):
- For \(x = -2, y = -4\), \(\frac{y}{x} = \frac{-4}{-2} = 2\)
- For \(x = -1, y = -2\), \(\frac{y}{x} = \frac{-2}{-1} = 2\)
- For \(x = 0, y = 0\), \(\frac{y}{x}\) is undefined (division by 0 is not possible)
- For \(x = 2, y = 0\), \(\frac{y}{x} = \frac{0}{2} = 0\)

Since the ratio is not constant (0 for one pair, 2 for others), this table **does not represent** a proportional relationship.

### Second Table:
\[
\begin{array}{c|c}
x & y \\
\hline
-2 & -3 \\
-1 & -2 \\
0  & -1 \\
2  & 0  \\
\end{array}
\]
Checking the ratio \(\frac{y}{x}\):
- For \(x = -2, y = -3\), \(\frac{y}{x} = \frac{-3}{-2} = 1.5\)
- For \(x = -1, y = -2\), \(\frac{y}{x} = \frac{-2}{-1} = 2\)
- For \(x = 0, y = -1\), \(\frac{y}{x}\) is undefined
- For \(x = 2, y = 0\), \(\frac{y}{x} = \frac{0}{2} = 0\)

The ratio is not constant, so this table also **does not represent** a proportional relationship.

### Third Table:
\[
\begin{array}{c|c}
x & y \\
\hline
-4 & -5 \\
-2 & -2.5 \\
0  & 0 \\
2  & 2.5 \\
4  & 5 \\
\end{array}
\]
Checking the ratio \(\frac{y}{x}\):
-

Which table represents a proportional relationship between y and x?

Analyze tables to determine which one represents a proportional relationship between x and y. Learn how to check ratios and identify proportional patterns. This exercise is suitable for Grade 7 students studying algebra and ratios.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation