Question

find the constant of proportionality k as a fraction in simplest form. then enter an equation for the relationship between x and y.

x	12	24	36	48
y	2	4	6	8

the constant of proportionality, k is equal to
the equation is y =

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \).

Step2: Calculate \( k \) using a pair of \( x \) and \( y \) values

Let's take the first pair \( x = 12 \) and \( y = 2 \). Then \( k=\frac{y}{x}=\frac{2}{12} \). Simplify this fraction by dividing numerator and denominator by their greatest common divisor, which is 2. So \( \frac{2\div2}{12\div2}=\frac{1}{6} \). We can check with other pairs: for \( x = 24 \), \( y = 4 \), \( \frac{4}{24}=\frac{1}{6} \); for \( x = 36 \), \( y = 6 \), \( \frac{6}{36}=\frac{1}{6} \); for \( x = 48 \), \( y = 8 \), \( \frac{8}{48}=\frac{1}{6} \). So \( k=\frac{1}{6} \).

Step3: Write the equation for the relationship

Using the formula \( y = kx \) and substituting \( k=\frac{1}{6} \), the equation is \( y=\frac{1}{6}x \).

Answer:

The constant of proportionality, \( k \) is equal to \(\frac{1}{6}\).
The equation is \( y = \frac{1}{6}x \).