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To find the equation of the line in slope-intercept form, we need to determine the slope (`m`) and the y-intercept (`b`).

### Step 1: Identify two points on the line
From the graph:
- The line appears to pass through the points \((-6, -4)\) and \((6, 3)\).

### Step 2: Calculate the slope (`m`)
The slope \(m\) is calculated using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the points \((-6, -4)\) and \((6, 3)\) into the formula:

\[
m = \frac{3 - (-4)}{6 - (-6)} = \frac{3 + 4}{6 + 6} = \frac{7}{12}
\]

### Step 3: Determine the y-intercept (`b`)
The slope-intercept form is:

\[
y = mx + b
\]

We can use one of the points to solve for \(b\). Let's use the point \((6, 3)\):

\[
3 = \frac{7}{12} \times 6 + b
\]

\[
3 = \frac{7 \times 6}{12} + b = \frac{42}{12} + b = 3.5 + b
\]

\[
b = 3 - 3.5 = -0.5
\]

### Step 4: Write the final equation
The equation of the line in slope-intercept form is:

\[
y = \frac{7}{12}x - \frac{1}{2}
\]

Would you like further details or have any questions?

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**Related Questions:**
1. How do you calculate the slope between two points on a graph?
2. What is the significance of the y-intercept in the slope-intercept form of a line?
3. How can you determine the equation of a line if you only know its slope and a single point?
4. What is the difference between the slope-intercept form and the point-slope form of a line?
5. How do you convert an equation from standard form to slope-intercept form?

**Tip:** When identifying points on a graph, choose points where the line crosses grid intersections to ensure more accurate calculations.

Write the equation of the line in fully simplified slope-intercept form.

Learn how to determine the equation of a line from a graph using the slope-intercept form. This problem involves finding the slope and y-intercept, crucial algebra concepts suitable for students in Grades 8-10.

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