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To write the equation of the line in slope-intercept form, we need to express it as:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Determine the slope (\(m\))
The slope \(m\) is calculated using the formula:

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

Looking at the graph:

- The line passes through the points \((-2, 2)\) and \((0, 0)\).
- Using these points, we can calculate the slope:

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

So, the slope of the line is \(m = -1\).

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

### Step 3: Write the equation
Now that we know the slope \(m = -1\) and the y-intercept \(b = 0\), the equation of the line is:

\[
y = -x
\]

This is the slope-intercept form of the equation for the line shown in the graph.

Do you need further details or clarifications on any part of this solution?

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Here are 5 related questions to expand your understanding:
1. How do you calculate the slope if the line passes through different points?
2. What would happen to the slope if the line were steeper or flatter?
3. How do you determine the equation of a vertical line?
4. How do you find the equation of a line parallel to this one?
5. What is the general form of a line's equation and how does it relate to the slope-intercept form?

**Tip**: Always check both the x- and y-coordinates when calculating the slope; a negative slope means the line is decreasing from left to right.

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

Learn how to determine the slope-intercept form of a line passing through the points (-2, 2) and (0, 0). This problem covers key algebraic concepts such as the slope formula and the slope-intercept form equation. Suitable for students in Grades 7-9.

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