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!