https://file.aiquickdraw.com/mathbot/file/1739554711468t8za2crz.jpg

The table in the image you provided lists the following pairs of \(x\) and \(y\) values:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
-5 & 25 \\
-4 & 18 \\
-3 & 11 \\
-2 & 4 \\
-1 & -3 \\
\hline
\end{array}
\]

To determine whether a linear or exponential function models the data, let's check the differences in \(y\) values.

### Checking for a Linear Function:
A linear function follows the form \(y = mx + b\), where the difference between consecutive \(y\) values should be constant. Let’s compute the differences between consecutive \(y\) values:

- \(18 - 25 = -7\)
- \(11 - 18 = -7\)
- \(4 - 11 = -7\)
- \(-3 - 4 = -7\)

Since the differences are constant (-7), this indicates that the data follows a **linear** relationship.

### Finding the Linear Function:
We can now find the equation of the line using the slope-intercept form \(y = mx + b\). The slope \(m\) is \(-7\), and we can use one of the points to find \(b\). Let’s use the point \((-5, 25)\):

\[
25 = -7(-5) + b
\]
\[
25 = 35 + b
\]
\[
b = 25 - 35 = -10
\]

Thus, the linear function that models this data is:

\[
y = -7x - 10
\]

If you have any further questions or need more details, feel free to ask!

### Further questions to explore:
1. How would you graph the equation \(y = -7x - 10\)?
2. What does the slope of the line represent in the context of the data?
3. Can you find the value of \(y\) for \(x = 0\) using this equation?
4. How would the equation change if the differences were not constant?
5. What is the significance of the y-intercept (\(b = -10\)) in this context?

### Tip:
Always check the differences in \(y\) when trying to identify if a relationship is linear or exponential. For linear, the difference is constant; for exponential, the ratios between consecutive \(y\) values are constant.

Look at this table:

x | y
-5 | 25
-4 | 18
-3 | 11
-2 | 4
-1 | -3

Write a linear function (y = mx + b) or an exponential function (y = a(b)^x) that models the data.

Learn how to identify and solve linear functions based on a given data table. The problem involves determining the linear function for a table of x and y values and understanding the concepts of slope and y-intercept. Suitable for students in Grades 7-9.

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