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To find the equation of the linear function in slope-intercept form, we need to determine the slope \( m \) and the y-intercept \( b \) from the given table.

The slope-intercept form of a line is:
\[
y = mx + b
\]

We calculate the slope \( m \) using two points from the table. Let's take the points \( (-1, 3) \) and \( (1, 5) \).

The formula for the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substitute the values:
\[
m = \frac{5 - 3}{1 - (-1)} = \frac{2}{2} = 1
\]
So, the slope \( m = 1 \).

Now, to find the y-intercept \( b \), we use one of the points and the slope we just found. Let's use the point \( (1, 5) \). Substitute into the slope-intercept form:
\[
5 = 1(1) + b
\]
\[
5 = 1 + b
\]
\[
b = 4
\]

Thus, the equation of the linear function is:
\[
y = x + 4
\]

Would you like more details or have any questions? Here are some related questions:

1. How can we verify the equation with other points in the table?
2. What happens if we use different points to calculate the slope?
3. How would the equation change if the slope were negative?
4. Can we derive the equation using the point-slope form instead?
5. How does the equation change if the table represents a different type of function?

**Tip:** Always double-check by substituting other points into your equation to ensure accuracy.

Find the equation of the linear function represented by the table below in slope-intercept form.

| x | y |
|----|----|
| -1 | 3 |
| 1  | 5 |
| 3  | 7 |
| 5  | 9 |

Learn how to find the equation of a linear function from a given table of values. This step-by-step example demonstrates how to determine the slope and y-intercept to write the equation in slope-intercept form (y = mx + b). Suitable for students in Grades 8-10.

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