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We can derive the equation of the line from the graph in **slope-intercept form**, which is:

\[
y = mx + b
\]

Where:
- \(m\) is the slope of the line.
- \(b\) is the y-intercept (where the line crosses the y-axis).

### Step 1: Find the slope (m)
The slope is the change in y divided by the change in x, or:

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

From the graph, we can use the two points:
- \( (0, -2) \)
- \( (1, 3) \)

Plugging these into the slope formula:

\[
m = \frac{3 - (-2)}{1 - 0} = \frac{5}{1} = 5
\]

So, the slope \(m = 5\).

### Step 2: Determine the y-intercept (b)
From the graph, we can see that the line crosses the y-axis at the point \( (0, -2) \). Therefore, the y-intercept \(b = -2\).

### Step 3: Write the equation
Now, we can substitute the slope \(m = 5\) and the y-intercept \(b = -2\) into the slope-intercept form:

\[
y = 5x - 2
\]

Thus, the equation of the line is:

\[
y = 5x - 2
\]

Would you like more details, or have any other questions? Here are some related questions you might consider:

1. What does the slope of a line represent in real-world scenarios?
2. How can we find the equation of a line given any two points?
3. How does changing the slope or intercept affect the graph of a line?
4. What is the point-slope form of the equation of a line, and how is it derived?
5. How can the slope-intercept form be used to solve real-life problems?

**Tip**: The slope of a line determines its steepness. A larger slope means the line is steeper, while a negative slope means the line slopes downward.

Use the graph to derive the equation of the line in slope-intercept form.

Learn how to find the equation of a line from a graph using slope-intercept form. This example includes step-by-step calculations for determining the slope and y-intercept using the points (0, -2) and (1, 3). Suitable for students in Grades 7-9.

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