To find the equation of the line that passes through the points $(-1,6)$ and $(-5,3)$, follow these steps:

Step 1: Find the Slope

The slope $m$ of a line passing 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 $(-1,6)$ as $(x_1, y_1)$ and $(-5,3)$ as $(x_2, y_2)$:

$m = \frac{3 - 6}{-5 - (-1)}$

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

Step 2: Use the Point-Slope Form

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

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

Using $m = \frac{3}{4}$ and the point $(-1,6)$:

$y - 6 = \frac{3}{4}(x + 1)$

Step 3: Convert to Slope-Intercept Form

Expanding:

$y - 6 = \frac{3}{4}x + \frac{3}{4}$

Adding 6 to both sides:

$y = \frac{3}{4}x + \frac{3}{4} + 6$

$y = \frac{3}{4}x + \frac{3}{4} + \frac{24}{4}$

$y = \frac{3}{4}x + \frac{27}{4}$

Final Answer:

$y = \frac{3}{4}x + \frac{27}{4}$

Would you like me to verify or explain any step in more detail?

---

Related Questions:

1. How do you convert from point-slope form to standard form?
2. What is the perpendicular line to this equation passing through $(0,0)$?
3. How can you determine if another point lies on this line?
4. How do you find the x- and y-intercepts of this equation?
5. What are parallel lines, and how can you find one parallel to this equation?

Tip: When finding the slope, always check the signs carefully to avoid calculation errors!