To determine the constant of proportionality in the equation [tex]\( y = 24x \)[/tex], we need to identify the coefficient of [tex]\( x \)[/tex] in the equation.
The equation [tex]\( y = 24x \)[/tex] represents a linear relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex]. In such equations, the constant of proportionality is the number that [tex]\( x \)[/tex] is multiplied by to yield [tex]\( y \)[/tex]. This constant is also known as the slope in the context of linear equations.
Here's a step-by-step outline to identify the constant of proportionality:
1. Identify the format of the equation:
The given equation is [tex]\( y = 24x \)[/tex].
2. Understand the structure:
In a linear equation of the form [tex]\( y = kx \)[/tex], [tex]\( k \)[/tex] represents the constant of proportionality. It is the factor by which [tex]\( x \)[/tex] is multiplied to produce [tex]\( y \)[/tex].
3. Extract the constant:
Comparing the given equation [tex]\( y = 24x \)[/tex] to the format [tex]\( y = kx \)[/tex], we see that [tex]\( k = 24 \)[/tex].
Therefore, the constant of proportionality in the equation [tex]\( y = 24x \)[/tex] is:
A. 24
