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To determine the equation of the line in slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), we will follow these steps:

### Step 1: Identify the slope (\(m\))
The slope is the rise over the run, or the change in \(y\) divided by the change in \(x\). From the graph:
- The line passes through the points \((-6, -4)\) and \((6, 6)\).

Using the formula for the slope:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (-4)}{6 - (-6)} = \frac{6 + 4}{6 + 6} = \frac{10}{12} = \frac{5}{6}
\]

So, the slope \(m = \frac{5}{6}\).

### Step 2: Identify the y-intercept (\(b\))
The y-intercept is the value of \(y\) when \(x = 0\). By inspecting the graph, we can see that the line crosses the y-axis at \((0, 1)\). Therefore, the y-intercept \(b = 1\).

### Final Equation
Substituting \(m = \frac{5}{6}\) and \(b = 1\) into the slope-intercept form equation:
\[
y = \frac{5}{6}x + 1
\]

Thus, the equation of the line is:
\[
y = \frac{5}{6}x + 1
\]

Would you like more details or have any other questions?

Here are 5 related questions to explore:
1. How can we convert this slope-intercept form into standard form?
2. What is the significance of the slope and y-intercept in real-world scenarios?
3. How would the equation change if the slope were negative?
4. What is the equation of a line parallel to this one?
5. How would you find the equation of a perpendicular line to this one?

**Tip:** Always verify points on the graph by substituting them into your final equation.

Write the equation of this line in slope-intercept form.

Learn how to find the slope-intercept form of a line from a graph, using points and the slope formula. The solution includes identifying the slope (m) and y-intercept (b) to write the equation y = mx + b. Suitable for Grades 7-9.

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