The y-intercept of the graph of y + 5 = −7(x + 5) in the xy-plane is (0, y). What is the value of y?

1. Break Down the Problem

We need to find the y-intercept of the equation $y + 5 = -7(x + 5)$. The y-intercept occurs when $x = 0$.

2. Relevant Concepts

To find y when $x = 0$, we will substitute $x = 0$ into the equation and solve for $y$.

3. Analysis and Detail

1. Substitute $x = 0$ into the equation: $y + 5 = -7(0 + 5)$ This simplifies to: $y + 5 = -7(5)$ $y + 5 = -35$

2. Now, solve for $y$: $y = -35 - 5$ $y = -40$

4. Verify and Summarize

After substituting and solving, we find the calculations are correct. The y-coordinate at the y-intercept is $-40$.

Final Answer

The value of $y$ at the y-intercept is $-40$. Thus, the y-intercept is $(0, -40)$.