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We are asked to find the equation of a line that passes through the point \( G(-4, 6) \) and has a slope of \( m = -3 \).

We can use the **point-slope form** of the equation of a line, which is given by:

\[
y - y_1 = m(x - x_1)
\]

where \( m \) is the slope and \( (x_1, y_1) \) is the point on the line. Substituting the values:

- \( m = -3 \)
- \( (x_1, y_1) = (-4, 6) \)

This gives us:

\[
y - 6 = -3(x + 4)
\]

Now, simplify the equation:

\[
y - 6 = -3x - 12
\]

Add 6 to both sides:

\[
y = -3x - 12 + 6
\]
\[
y = -3x - 6
\]

Thus, the equation of the line is:

\[
y = -3x - 6
\]

Looking at the options provided, the correct answer is **Option A**: \( y = -3x - 6 \).

Would you like more details or have any questions? Here are some related questions:

1. How can we derive the slope-intercept form of a line from other points and slopes?
2. What is the significance of the point-slope form in geometry?
3. How would the equation change if the slope was positive instead of negative?
4. Can we determine parallel lines from this equation? How?
5. How do you convert an equation in point-slope form to standard form?

**Tip:** The point-slope form is very useful for writing equations of lines when you know a point and the slope.

What is the equation of the line that passes through point G(-4, 6) and has a slope of -3?

Learn how to find the equation of a line passing through point G(-4, 6) and having a slope of -3. This problem uses the point-slope form of a linear equation and simplifies to give the final equation y = -3x - 6. Suitable for students in Grades 8-10.

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