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To write 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 can follow these steps:

### Step 1: Find the Slope (\(m\))
The slope is calculated as the "rise over run," or the change in \(y\) over the change in \(x\). From the graph:

- The line passes through two clear points: \( (0, -2) \) and \( (3, 4) \).
- The slope \(m\) is calculated by using the formula:
\[
m = \frac{\Delta y}{\Delta x} = \frac{4 - (-2)}{3 - 0} = \frac{6}{3} = 2
\]

### Step 2: Find the y-intercept (\(b\))
The y-intercept is where the line crosses the y-axis, which happens at the point \( (0, -2) \). So, \( b = -2 \).

### Step 3: Write the Equation
Now that we have the slope and the y-intercept, the equation of the line is:
\[
y = 2x - 2
\]

Would you like further details on any of these steps?

### Expanding Questions:
1. How do you calculate the slope between two points on a line?
2. What are the characteristics of a line with a positive slope like this one?
3. What does the y-intercept represent in the slope-intercept form?
4. How can you verify the slope by checking more points on the graph?
5. How do you convert between slope-intercept form and standard form?

### Tip:
Always pick two clear points on the line to avoid calculation errors when determining the slope.

Write the slope-intercept form of the equation of each line based on the graph provided.

Learn how to find the slope-intercept form of a line equation using graph points. This example covers slope calculation, identifying the y-intercept, and writing the equation in the form y = mx + b.

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