The equation of a line that is parallel to another line will have the same slope.

First, let's rewrite the equation of the given line $x + y = 7$ in slope-intercept form, $y = mx + b$, where $m$ is the slope:

$x + y = 7 \quad \text{(subtract } x \text{ from both sides)}$ $y = -x + 7$

From this equation, we can see that the slope $m$ of the line is $-1$.

Now, since we want the equation of a line parallel to this one, the slope of our new line will also be $m = -1$.

Next, we use the point-slope form of a line, which is given by:

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

Here, $(x_1, y_1) = (-1, -4)$ is the point through which the line passes, and $m = -1$. Plugging these values into the equation:

$y - (-4) = -1(x - (-1))$ $y + 4 = -1(x + 1)$ $y + 4 = -x - 1$ $y = -x - 1 - 4$ $y = -x - 5$

Thus, the equation of the line is:

$y = -x - 5$

Would you like further details or have any questions?

Here are five related questions you can explore:

1. How do you convert a line from standard form to slope-intercept form?
2. What is the point-slope form of a line, and when is it useful?
3. How do you find the slope of a line given two points?
4. What does it mean for two lines to be parallel?
5. How can you find the equation of a line perpendicular to a given line?

Tip: The slope-intercept form, $y = mx + b$, is often the easiest way to graph a line since it directly gives the slope and the y-intercept.