Problem

Write an equation in the form $y=m x+b$ for the following table:
\begin{tabular}{|c|c|}
\hline$x$ & $y$ \\
\hline-8 & -37 \\
\hline-6 & -25 \\
\hline-4 & -13 \\
\hline-2 & -1 \\
\hline 0 & 11 \\
\hline 2 & 23 \\
\hline 4 & 35 \\
\hline 6 & 47 \\
\hline
\end{tabular}
\[
y=
\]
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Answer

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Answer

Final Answer: \(\boxed{y = 6x + 11}\)

Steps

Step 1 :The equation of a line in the form \(y = mx + b\) is determined by the slope (m) and the y-intercept (b). The slope can be calculated by taking any two points from the table and using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). The y-intercept (b) is the value of y when x is 0. From the table, we can see that when x is 0, y is 11. So, b = 11.

Step 2 :Let's calculate the slope using the first two points in the table: (-8, -37) and (-6, -25).

Step 3 :m = 6.0

Step 4 :b = 11

Step 5 :The slope of the line is 6 and the y-intercept is 11. Therefore, the equation of the line in the form \(y = mx + b\) is \(y = 6x + 11\).

Step 6 :Final Answer: \(\boxed{y = 6x + 11}\)

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