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Look at this table:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
3 & -19 \\
\hline
4 & -28 \\
\hline
5 & -37 \\
\hline
6 & -46 \\
\hline
7 & -55 \\
\hline
\end{tabular}

Write a linear [tex]$(y=mx+b)$[/tex], quadratic [tex]$\left(y=ax^2\right)$[/tex], or exponential [tex]$\left(y=a(b)^x\right)$[/tex] function that models the data.

[tex]\[ y = \][/tex]
[tex]\[ \boxed{\phantom{answer}} \][/tex]



Answer :

GinnyAnswer
Sure! Let's analyze the given table of data points to determine the most suitable function to model the data.

[tex]\[ \begin{array}{|c|c|} \hline x & y \\ \hline 3 & -19 \\ \hline 4 & -28 \\ \hline 5 & -37 \\ \hline 6 & -46 \\ \hline 7 & -55 \\ \hline \end{array} \][/tex]

We aim to determine a linear function of the form [tex]\(y = mx + b\)[/tex].

Here are the steps to define the linear function:

1. Identify the slope ([tex]\(m\)[/tex]):
[tex]\[ m = -9.000000000000002 \][/tex]

2. Identify the y-intercept ([tex]\(b\)[/tex]):
[tex]\[ b = 7.999999999999996 \][/tex]

3. Construct the linear function:
Substitute the values of [tex]\(m\)[/tex] and [tex]\(b\)[/tex] into the linear function formula [tex]\(y = mx + b\)[/tex]:
[tex]\[ y = -9x + 8 \][/tex]

This linear equation accurately models the given data points from the table. Note this form, where the slope is [tex]\(-9\)[/tex] and the y-intercept is [tex]\(8\)[/tex].

So, the function that models the data is:

[tex]\[ y = -9x + 8 \][/tex]

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