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Use the graph of the line below to find the equation of the line.

To find the equation of the line shown in the graph, we'll first identify two key pieces of information: the slope (\(m\)) and the y-intercept (\(b\)).

### Step 1: Determine the Slope (\(m\))
The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. 

From the graph:
- One point on the line is \((-5, 5)\).
- Another point is \((5, -5)\).

Using these points, the slope \(m\) is calculated as follows:
\[
m = \frac{\text{rise}}{\text{run}} = \frac{-5 - 5}{5 - (-5)} = \frac{-10}{10} = -1
\]

### 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 \( (0, 0) \), so the y-intercept \(b = 0\).

### Step 3: Write the Equation
Now that we have the slope \(m = -1\) and the y-intercept \(b = 0\), the equation of the line in slope-intercept form \(y = mx + b\) is:
\[
y = -x
\]

So, the equation of the line is \(y = -x\).

Would you like any further details or explanations on this? Here are some additional related questions you might consider:

1. How would the equation change if the slope were positive?
2. What is the significance of the y-intercept in a linear equation?
3. How can you use the equation to find the x-intercept?
4. What would happen if the slope were zero?
5. How does the slope affect the angle of the line relative to the x-axis?

**Tip:** Remember that the slope of a line indicates its steepness and direction. A negative slope means the line goes down as you move from left to right.

Learn how to find the equation of a line from its graph using the slope and y-intercept. This problem involves understanding linear equations, calculating slopes, and determining y-intercepts. Suitable for Grades 7-9 students.

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