To identify the slope and the y-intercept from the given equation $y + 4 = -9(x - 3)$, we first need to rearrange the equation into the slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Let's work through the steps:

1. Distribute the $-9$ on the right-hand side: $y + 4 = -9x + 27$

2. Isolate $y$ by subtracting 4 from both sides: $y = -9x + 27 - 4$

3. Simplify the equation: $y = -9x + 23$

From this equation, we can see that:

• Slope $m = -9$
• Y-intercept $b = 23$

So, the slope is $-9$ and the y-intercept is $23$.

Would you like further details or have any questions?

Here are some related questions to consider:

1. How can you determine the slope of a line from two given points?
2. What does the y-intercept represent in a real-world context?
3. How would you graph the line $y = -9x + 23$ on a coordinate plane?
4. What is the significance of the slope in terms of the steepness of the line?
5. How can you convert a standard form equation to slope-intercept form?

Tip: Remember, the slope $m$ represents the rate of change of $y$ with respect to $x$, and the y-intercept $b$ is where the line crosses the y-axis.