To find the coefficient of the equation [tex]\( y = 4.2x \)[/tex], we need to identify the constant value that multiplies [tex]\( x \)[/tex] to give [tex]\( y \)[/tex]. This coefficient, or constant of proportionality, is the factor directly in front of the variable [tex]\( x \)[/tex].
Let's analyze the given equation step-by-step:
1. The equation provided is [tex]\( y = 4.2x \)[/tex].
2. By examining the structure of the equation, we observe that each value of [tex]\( y \)[/tex] is obtained by multiplying [tex]\( x \)[/tex] by a constant factor.
To further verify our understanding:
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 4.2 \times 0 = 0
\][/tex]
- For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 4.2 \times 2 = 8.4
\][/tex]
- For [tex]\( x = 4 \)[/tex]:
[tex]\[
y = 4.2 \times 4 = 16.8
\][/tex]
- For [tex]\( x = 6 \)[/tex]:
[tex]\[
y = 4.2 \times 6 = 25.2
\][/tex]
Comparing these calculations with the values in the provided table confirms that each [tex]\( y \)[/tex] matches the pattern [tex]\( y = 4.2x \)[/tex].
Therefore, the coefficient of the equation, or the constant of proportionality, is [tex]\( 4.2 \)[/tex].
So, the coefficient of the equation or constant of proportionality is [tex]\( \boxed{4.2} \)[/tex].
