The image provides two points, $(-4, -2)$ and $(-3, 5)$, through which we need to determine a line. To find the equation of the line passing through these points, we can follow these steps:

Step 1: Find the slope $m$

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substituting the given points $(-4, -2)$ and $(-3, 5)$:

$m = \frac{5 - (-2)}{-3 - (-4)} = \frac{5 + 2}{-3 + 4} = \frac{7}{1} = 7$

Step 2: Use point-slope form to find the equation of the line

The point-slope form of a line is given by:

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

Using the slope $m = 7$ and the point $(-4, -2)$:

$y - (-2) = 7(x - (-4))$ $y + 2 = 7(x + 4)$

Step 3: Simplify the equation

Distribute and simplify:

$y + 2 = 7x + 28$ $y = 7x + 28 - 2$ $y = 7x + 26$

Thus, the equation of the line passing through $(-4, -2)$ and $(-3, 5)$ is:

$y = 7x + 26$

Would you like more details on this, or do you have any questions?

Here are 5 related questions for further exploration:

1. How would the equation change if we used a different point?
2. Can you find the equation of a line parallel to this one?
3. What would be the equation of a line perpendicular to this one?
4. How do we interpret the slope of this line geometrically?
5. What are the intercepts of the line with the x-axis and y-axis?

Tip: The slope of a line represents how much $y$ changes for every unit change in $x$.