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To find the equation of the line in slope-intercept form (\(y = mx + b\)), we need to determine the slope (\(m\)) and the y-intercept (\(b\)).

### Step 1: Determine the slope (\(m\))
The slope is calculated using the formula:
\[
m = \frac{\text{rise}}{\text{run}}
\]
From the graph, let's identify two points that the line passes through. It seems that the line passes through \((0, 6)\) and \((6, 0)\).

- **Rise**: The vertical change is \(6\) units down.
- **Run**: The horizontal change is \(6\) units to the right.

Thus, the slope is:
\[
m = \frac{-6}{6} = -1
\]

### Step 2: Determine the y-intercept (\(b\))
The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at \(6\), so \(b = 6\).

### Step 3: Write the equation
With \(m = -1\) and \(b = 6\), the equation of the line in slope-intercept form is:
\[
y = -x + 6
\]

Would you like more details or have any questions?

Here are five related questions to further your understanding:
1. How would the equation change if the line had a different y-intercept?
2. Can you find the equation if the line had a slope of 2 and passed through the origin?
3. What would be the equation if the line was vertical or horizontal?
4. How does changing the slope affect the steepness of the line?
5. How can we determine the equation if given only the slope and a point on the line?

**Tip:** When determining the slope from a graph, choose two points that lie exactly on grid intersections for more accurate calculations.

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

Learn how to write the equation of a line in slope-intercept form from a graph. The line passes through the points (0, 6) and (6, 0), with a slope of -1 and a y-intercept of 6. Suitable for students in Grades 7-10.

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