What is the slope of the line given by the equation below?y + 2 = -3(x - 5)A.-3B.-5C.3D.2

1. Break Down the Problem

We need to find the slope of the line given by the equation $y + 2 = -3(x - 5)$. The first step is to rearrange this equation into the slope-intercept form $y = mx + b$, where $m$ represents the slope.

2. Relevant Concepts

The slope-intercept form of a linear equation is given by: $y = mx + b$ where $m$ is the slope.

3. Analysis and Detail

Let's manipulate the equation: $y + 2 = -3(x - 5)$ Distributing on the right side: $y + 2 = -3x + 15$ Now, isolate $y$: $y = -3x + 15 - 2$ $y = -3x + 13$ From this form, we can see that the slope $m$ is $-3$.

4. Verify and Summarize

Checking the slope from the equation: it is consistent with the manipulation steps completed. Thus, the slope of the line is confirmed.

Final Answer

The slope of the line is $-3$, so the correct answer is A. -3.