To find the equation of a line parallel to $y = -12x$ that passes through the point $(8, -2)$, follow these steps:

---

Step 1: Identify the slope

The given line is $y = -12x$, which is in slope-intercept form ($y = mx + b$). Here, the slope ($m$) is $-12$.

Since parallel lines have the same slope, the line we are looking for also has a slope of $-12$.

---

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

The point-slope form of a line is: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a point on the line, and $m$ is the slope.

Substituting $m = -12$, $x_1 = 8$, and $y_1 = -2$, we get: $y - (-2) = -12(x - 8)$

Simplify: $y + 2 = -12(x - 8)$

---

Step 3: Simplify to slope-intercept form (if needed)

Distribute $-12$: $y + 2 = -12x + 96$

Subtract 2 from both sides: $y = -12x + 94$

---

Final Answer:

The equation of the line is: $y = -12x + 94$

---

Would you like further explanation or clarification?
Here are some related questions for further practice:

1. What is the equation of a line perpendicular to $y = -12x$ and passing through $(8, -2)$?
2. How do you derive the equation of a line given two points instead of a slope and a point?
3. Can you verify if the point $(10, -26)$ lies on the line $y = -12x + 94$?
4. How do you find the x-intercept and y-intercept of the line $y = -12x + 94$?
5. What is the slope of a line that is neither parallel nor perpendicular to $y = -12x$?

Tip:

To confirm your equation, substitute the given point into your final equation to ensure it satisfies the line!