To write the equation $y + 7 = -32(x + 1)$ in standard form, we aim for the form:

$Ax + By = C$

where $A$, $B$, and $C$ are integers, and $A \geq 0$.

Steps to Convert:

1. Start with the given equation: $y + 7 = -32(x + 1)$

2. Expand the right-hand side: $y + 7 = -32x - 32$

3. Subtract $7$ from both sides to isolate $y$: $y = -32x - 39$

4. Rearrange to standard form by moving all terms involving $x$ and $y$ to one side: $32x + y = -39$

Final Answer:

$32x + y = -39$

This is the standard form of the given equation.

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Related Questions:

1. What is the slope and y-intercept of the equation in standard form?
2. How do you convert from slope-intercept form to standard form?
3. Can you graph the equation using its standard form?
4. What are the x- and y-intercepts of this equation?
5. How do you verify that the conversion to standard form is correct?

Tip:

When converting to standard form, ensure all coefficients are integers, and if $A$ is negative, multiply through by $-1$ to make it positive.