To find the equation of the line that passes through the points $(-5, -4)$ and $(5, 1)$, we can follow these steps:

Step 1: Find the slope of the line

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the points $(-5, -4)$ and $(5, 1)$:

$m = \frac{1 - (-4)}{5 - (-5)} = \frac{1 + 4}{5 + 5} = \frac{5}{10} = \frac{1}{2}$

So, the slope $m = \frac{1}{2}$.

Step 2: Use the point-slope form of the equation

The point-slope form of the equation of a line is:

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

We can use either point. Let's use the point $(-5, -4)$.

$y - (-4) = \frac{1}{2}(x - (-5))$

Simplifying:

$y + 4 = \frac{1}{2}(x + 5)$

Step 3: Simplify the equation

Distribute the $\frac{1}{2}$ on the right-hand side:

$y + 4 = \frac{1}{2}x + \frac{5}{2}$

Now, subtract 4 from both sides:

$y = \frac{1}{2}x + \frac{5}{2} - 4$

Convert $4$ to a fraction with denominator 2:

$y = \frac{1}{2}x + \frac{5}{2} - \frac{8}{2}$

Simplify:

$y = \frac{1}{2}x - \frac{3}{2}$

Final Equation:

The equation of the line is:

$y = \frac{1}{2}x - \frac{3}{2}$

Would you like further details or any clarifications? Here are a few related questions to explore:

1. How do you graph the equation of a line?
2. What is the intercept form of the equation of a line?
3. How can you calculate the distance between two points on a line?
4. How do you determine the slope of a line from a graph?
5. What is the relationship between slope and parallel/perpendicular lines?

Tip: Always double-check your calculations for signs when using the slope formula. A small error in the calculation of the slope can affect the final equation!