Question

the table shows the side lengths and perimeters of four squares.

which equation represents the relationship between the side length, \\(x\\), and the perimeter, \\(y\\)?

\\(y = \frac{1}{4}x\\)
\\(y = 4x\\)
\\(y = x + 13.5\\)
\\(y = x - 13.5\\)

Explanation:

Identify the variables and given data

Using the Linear Equation from Table knowledge point
The table provides pairs of values representing the side length \(x\) and the perimeter \(y\) of four squares:

• \((4.5, 18)\)
• \((8.5, 34)\)
• \((10.25, 41)\)
• \((13.75, 55)\)

Determine the constant of proportionality

Using the Linear Equation from Table knowledge point

$$
LATEXBLOCK0
$$

Formulate the linear equation

Using the Linear Equation from Table knowledge point

$$ y = 4x $$

Answer:

• (A) \(y = \frac{1}{4}x\)
• (B) \(y = 4x\) (Correct answer)
• (C) \(y = x + 13.5\)
• (D) \(y = x - 13.5\)