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To find the equation of the line that passes through the point \((-3, 6)\) and has a slope of \(-4\), we can use the point-slope form of a linear equation:

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

Where:
- \((x_1, y_1)\) is the given point.
- \(m\) is the slope.

Plugging in the values \((x_1, y_1) = (-3, 6)\) and \(m = -4\):

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

Now, distribute the slope \(-4\) to both \(x\) and \(3\):

\[ y - 6 = -4x - 12 \]

Finally, solve for \(y\) by adding 6 to both sides:

\[ y = -4x - 12 + 6 \]
\[ y = -4x - 6 \]

The equation of the line is:

\[ y = -4x - 6 \]

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

Here are 5 related questions to expand on this topic:

1. How do you find the equation of a line if given two points instead of one point and a slope?
2. What is the significance of the y-intercept in the equation of a line?
3. How would the equation change if the slope were positive instead of negative?
4. How can you convert the point-slope form into the slope-intercept form?
5. What does the slope of a line indicate about its direction and steepness?

**Tip:** To easily switch between different forms of linear equations, practice using the point-slope, slope-intercept, and standard forms with different problems.

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

Learn how to find the equation of a line that passes through the point (-3, 6) with a slope of -4 using the point-slope formula. This example walks through converting the point-slope form to slope-intercept form, explaining each step in detail. Suitable for students in Grades 8-10.

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