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The equation given is \( y - 6 = -(x - 4) \), which can be rearranged into slope-intercept form to better analyze which graph represents it.

### Step 1: Simplify the given equation
Start with the original equation:
\[
y - 6 = -(x - 4)
\]

Distribute the negative sign on the right-hand side:
\[
y - 6 = -x + 4
\]

Now, add 6 to both sides to isolate \( y \):
\[
y = -x + 4 + 6
\]

Simplify:
\[
y = -x + 10
\]

### Step 2: Identify the slope and intercept
- The slope (\( m \)) is \( -1 \), meaning the line slopes downward at a 45° angle.
- The y-intercept (\( b \)) is 10, meaning the line crosses the y-axis at \( (0, 10) \).

### Step 3: Match with the graph
We are looking for a graph with a line that:
- Starts at \( (0, 10) \) on the y-axis.
- Has a slope of \( -1 \), meaning for every 1 unit increase in \( x \), the value of \( y \) decreases by 1 unit.

Looking at the graph you provided, the top graph seems to match the description:
- It crosses the y-axis at \( (0, 10) \).
- The line slopes downward with a slope of \( -1 \).

Thus, the top graph represents the equation \( y = -x + 10 \).

Would you like more details on this process? Here are some related questions:

1. What is the process of converting an equation to slope-intercept form?
2. How do you calculate the slope from a graph?
3. Can you explain how transformations (translations and reflections) affect the graph of a line?
4. How do negative slopes differ from positive slopes in visual terms?
5. How does the y-intercept influence where a line crosses the y-axis?

**Tip**: Always try to simplify an equation to its slope-intercept form \( y = mx + b \) for easier graphing!

Which graph represents the equation y - 6 = -(x - 4)?

Learn how to graph the linear equation y - 6 = -(x - 4) by converting it into slope-intercept form. This problem teaches important concepts such as identifying the slope and y-intercept for graphing. Suitable for students in Grades 7-10.

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