To find the equation of a line that passes through the two points $(-1, -6)$ and $(3, 4)$, we can follow these steps:

Step 1: Find the slope of the line

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

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

Substituting the given points $(-1, -6)$ and $(3, 4)$:

$m = \frac{4 - (-6)}{3 - (-1)} = \frac{4 + 6}{3 + 1} = \frac{10}{4} = 2.5$

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

The point-slope form is:

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

Substitute $m = 2.5$ and one of the points, say $(-1, -6)$:

$y - (-6) = 2.5(x - (-1))$

Simplifying:

$y + 6 = 2.5(x + 1)$

Step 3: Simplify to slope-intercept form

Now, expand and simplify the equation:

$y + 6 = 2.5x + 2.5$

$y = 2.5x + 2.5 - 6$

$y = 2.5x - 3.5$

So, the equation of the line in slope-intercept form is:

$y = 2.5x - 3.5$

Would you like more details or have any questions about this solution?

Here are 5 related questions you might find useful:

1. How do you find the equation of a line given the slope and a point?
2. Can you convert the equation into standard form?
3. What is the significance of the slope in the context of a real-world scenario?
4. How do you find the y-intercept of a line given two points?
5. What happens if the two points are vertical? How would the equation of the line change?

Tip: Always start by calculating the slope when given two points on a line, as it helps to form the equation step by step!