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To find the equation of the linear function represented by the table in slope-intercept form, we need to calculate the slope (\( m \)) and y-intercept (\( b \)) of the line.

The table provides these pairs of \((x, y)\) values:
- \((-4, -21)\)
- \((1, -1)\)
- \((6, 19)\)
- \((11, 39)\)

### Step 1: Calculate the Slope (\( m \))
The slope \( m \) is found using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let's use the points \((1, -1)\) and \((6, 19)\) from the table:
\[
m = \frac{19 - (-1)}{6 - 1} = \frac{19 + 1}{5} = \frac{20}{5} = 4
\]

So, the slope \( m = 4 \).

### Step 2: Find the y-Intercept (\( b \))
With the slope \( m = 4 \), we can use the slope-intercept form \( y = mx + b \) with one of the points to solve for \( b \).

Using the point \((1, -1)\):
\[
-1 = 4(1) + b
\]
\[
-1 = 4 + b
\]
\[
b = -1 - 4 = -5
\]

### Conclusion
The equation of the line in slope-intercept form is:
\[
y = 4x - 5
\]

Would you like more details, or do you have any questions?

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### Further Practice Questions
1. Verify the equation \( y = 4x - 5 \) with the other points in the table.
2. Find the slope-intercept form if the points were \((-2, -13)\) and \((2, 5)\).
3. Convert \( y = 4x - 5 \) to standard form \( Ax + By = C \).
4. Determine the y-intercept of a line with slope \( -3 \) passing through \( (0, 4) \).
5. Calculate the slope of a line passing through \((5, 10)\) and \((10, 25)\).

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### Tip
When finding the equation of a line from a table, always start by calculating the slope using any two points. This will help you check if the relationship is indeed linear.

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

Learn how to find the equation of a linear function represented by a table of values. This guide explains how to calculate the slope and y-intercept, covering key algebraic concepts and formulas. Ideal for students in Grades 8-10.

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