To graph the equation $y + 4 = -5(x - 5)$, we first need to rewrite it in slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Simplify the equation

We start with:

$y + 4 = -5(x - 5)$

First, distribute the $-5$ on the right-hand side:

$y + 4 = -5x + 25$

Next, subtract 4 from both sides to isolate $y$:

$y = -5x + 25 - 4$

$y = -5x + 21$

Now, we have the equation in slope-intercept form:

$y = -5x + 21$

Step 2: Graph the line

• Slope $m = -5$: This means for every 1 unit increase in $x$, $y$ decreases by 5 units.
• Y-intercept $b = 21$: The line crosses the y-axis at $y = 21$.

Graphing Steps:

1. Start at the y-intercept (0, 21) on the graph.
2. From there, use the slope $-5$ to plot another point. From $(0, 21)$, move 1 unit to the right (positive $x$) and 5 units down (negative $y$) to the point $(1, 16)$.
3. Draw a straight line through the points $(0, 21)$ and $(1, 16)$.

If you want, I can generate the graph for you. Would you like that?