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The question asks for the equation of the line shown in slope-intercept form, which is:

\[
y = mx + b
\]

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

### Step 1: Find the Slope (\( m \))
The slope is calculated as:

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

From the graph:
- One point on the line is \( (0, -1) \), the y-intercept.
- Another point is \( (3, 2) \).

Now, calculate the slope:

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

So, the slope \( m = 1 \).

### Step 2: Find the Y-Intercept (\( b \))
The y-intercept is the point where the line crosses the y-axis. From the graph, this occurs at \( y = -1 \).

### Step 3: Write the Equation
Substitute the values of \( m \) and \( b \) into the slope-intercept form:

\[
y = 1x - 1
\]

Thus, the equation of the line is:

\[
y = x - 1
\]

Do you want further details or have any questions about this? 

Here are 5 related questions to deepen your understanding:
1. What would happen if the slope was negative?
2. How do you find the equation if you only know two points?
3. How can you verify the correctness of the equation from the graph?
4. What does the slope tell you about the direction of the line?
5. How do you convert the equation to standard form?

**Tip**: The slope describes the rate of change of the line, telling you how steep the line is and its direction (positive or negative slope).

Write the slope-intercept form for the line shown in the graph.

Learn how to find the slope-intercept form of a line from a graph. In this problem, students will use the formula y = mx + b and apply the slope formula to find the equation of the line, y = x - 1. This exercise is suitable for Grades 8-10 and covers key concepts in algebra and graphing.

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