To find the equation of a line passing through two given points $(1, 3)$ and $(-3, -1)$, we can follow these steps:

Step 1: Find the slope (m)

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

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

Substitute $(x_1, y_1) = (1, 3)$ and $(x_2, y_2) = (-3, -1)$ into the formula:

$m = \frac{-1 - 3}{-3 - 1} = \frac{-4}{-4} = 1$

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

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

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

We can use either of the given points. Let's use $(1, 3)$:

$y - 3 = 1(x - 1)$

Simplify the equation:

$y - 3 = x - 1$

$y = x + 2$

Final equation:

The equation of the line passing through the points $(1, 3)$ and $(-3, -1)$ is:

$y = x + 2$

Would you like further clarification or a different approach? Here are 5 related questions to extend your understanding:

1. How do we find the equation of a vertical or horizontal line?
2. Can the slope of a line ever be undefined? If so, what does it mean?
3. What is the difference between point-slope form and slope-intercept form?
4. How would the equation change if the points were reversed?
5. How do you find the midpoint of two points?

Tip: The slope of a line indicates how steep the line is. A positive slope means the line rises, while a negative slope means it falls.