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\begin{tabular}{|c|c|c|c|c|c|}
\hline
[tex]$x$[/tex] & 3 & 6 & 9 & 12 & 15 \\
\hline
[tex]$y$[/tex] & [tex]$\frac{17}{7}$[/tex] & [tex]$\frac{32}{7}$[/tex] & [tex]$\frac{47}{7}$[/tex] & [tex]$\frac{62}{7}$[/tex] & [tex]$\frac{77}{7}$[/tex] \\
\hline
\end{tabular}

Given the table of values, which equation shows the relationship between [tex]$x$[/tex] and [tex]$y$[/tex]?



Answer :

GinnyAnswer
To find the equation that describes the relationship between \( x \) and \( y \) for the given values, we can determine the linear relationship by finding the slope (\( m \)) and the y-intercept (\( b \)) using the least squares method.

Given data:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & 3 & 6 & 9 & 12 & 15 \\ \hline y & \frac{17}{7} & \frac{32}{7} & \frac{47}{7} & \frac{62}{7} & \frac{77}{7} \\ \hline \end{array} \][/tex]

1. Calculate the slope \( m \):
The slope (\( m \)) is calculated by determining the rate of change in \( y \) with respect to \( x \).

2. Calculate the y-intercept \( b \):
The y-intercept (\( b \)) is found where the line intersects the y-axis.

After performing the necessary computations, the results are:
- The slope \( m = 0.7142857142857144 \)
- The y-intercept \( b = 0.2857142857142819 \)

3. Formulate the equation of the line:
The equation of a line in its general form is:
[tex]\[ y = mx + b \][/tex]

Substituting the values of \( m \) and \( b \) into this equation, we get:
[tex]\[ y = 0.7142857142857144x + 0.2857142857142819 \][/tex]

Thus, the equation that shows the relationship between \( x \) and \( y \) based on the given table of values is:
[tex]\[ y = 0.7142857142857144x + 0.2857142857142819 \][/tex]

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