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Consider the equation [tex]\( y = 4.2x \)[/tex] and the table below that represents this relationship.

[tex]\[
\begin{tabular}{|c|c|}
\hline
$x$ & $y$ \\
\hline
0 & 0 \\
\hline
2 & 8.4 \\
\hline
4 & 16.8 \\
\hline
6 & 25.2 \\
\hline
\end{tabular}
\][/tex]

The coefficient of the equation or constant of proportionality is [tex]\(\boxed{\phantom{0}}\)[/tex].



Answer :

GinnyAnswer
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].

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