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We are given a point \((-1, 6)\) and a slope of \(-1\), and we need to find the equation of the line.

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

Given:
- \(x_1 = -1\)
- \(y_1 = 6\)
- \(m = -1\)

Substitute these values into the point-slope form equation:
\[
y - 6 = -1(x - (-1))
\]
Simplify:
\[
y - 6 = -1(x + 1)
\]
Distribute the \(-1\):
\[
y - 6 = -x - 1
\]
Now solve for \(y\):
\[
y = -x - 1 + 6
\]
\[
y = -x + 5
\]

So, the equation of the line is:
\[
y = -x + 5
\]

Let me know if you'd like any further details or explanations! 

Here are some related questions:
1. How do you convert between different forms of a line equation (e.g., point-slope, slope-intercept)?
2. What is the general equation of a line passing through two given points?
3. How can you determine the slope if you are given two points?
4. What is the equation of a line parallel to a given line with a different point?
5. How can you calculate the distance between a point and a line?

**Tip:** Understanding how to convert between point-slope and slope-intercept form is key to flexibility in solving various line equation problems.

What is the equation of the line that passes through the point (-1, 6) and has a slope of -1?

Learn how to find the equation of a line that passes through the point (-1, 6) with a slope of -1. This problem demonstrates how to use the point-slope and slope-intercept forms of a linear equation. Suitable for students in Grades 8-10.

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