To find the constant of proportionality in the equation [tex]\( y = \frac{1}{2} x \)[/tex], we need to identify the coefficient of [tex]\( x \)[/tex]. Here's a step-by-step breakdown:
1. Identify the form of the equation representing proportional relationships: A proportional relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] can be expressed in the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
2. Compare the given equation to the proportional form: The given equation is [tex]\( y = \frac{1}{2} x \)[/tex].
3. Spot the coefficient of [tex]\( x \)[/tex]: In the equation [tex]\( y = \frac{1}{2} x \)[/tex], the coefficient of [tex]\( x \)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
4. Determine the constant of proportionality: The coefficient of [tex]\( x \)[/tex] in the equation [tex]\( y = \frac{1}{2} x \)[/tex] is [tex]\(\frac{1}{2}\)[/tex], which means the constant of proportionality [tex]\( k \)[/tex] is [tex]\( 0.5 \)[/tex] when expressed as a decimal.
Thus, the constant of proportionality is:
[tex]\[ \text{constant of proportionality} = 0.5 \][/tex]
