To find the equation of the line passing through the point $(-1, -4)$ and parallel to the line $x + y = 7$, follow these steps:

Step 1: Find the slope of the given line

We rewrite the equation $x + y = 7$ in slope-intercept form $y = mx + b$.

$y = -x + 7$

The slope $m$ of this line is $-1$.

Step 2: Use the slope of the parallel line

Since parallel lines have the same slope, the line passing through $(-1, -4)$ will also have a slope $m = -1$.

Step 3: Write the equation using point-slope form

The point-slope form of a line is:

$y - y_1 = m(x - x_1)$

where $(x_1, y_1) = (-1, -4)$ is the given point, and $m = -1$ is the slope.

$y - (-4) = -1(x - (-1))$

Simplify:

$y + 4 = -1(x + 1)$

Step 4: Simplify to slope-intercept form

Distribute:

$y + 4 = -x - 1$

Now, isolate $y$:

$y = -x - 1 - 4$

$y = -x - 5$

Step 5: Final Equation

The equation of the line passing through $(-1, -4)$ and parallel to $x + y = 7$ is:

$y = -x - 5$

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Would you like to see more steps, or do you have any questions?

Here are 5 follow-up questions you may find helpful:

1. How do you find the slope of a line given two points?
2. What is the difference between parallel and perpendicular slopes?
3. How do you convert from point-slope form to standard form?
4. What happens if two lines have the same slope but different intercepts?
5. How can you verify if two lines are parallel using algebra?

Tip: When two lines are parallel, their slopes are identical but their intercepts differ.