What is the equation of the line that passes through the point left parenthesis, 4, comma, minus, 6, right parenthesis(4,−6) and has a slope of minus, 1−1?

To find the equation of a line that passes through the point \((4, -6)\) with a slope of \(-1\), we use the point-slope form of a line equation:

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

where:
- \( m \) is the slope of the line.
- \( (x_1, y_1) \) is a point on the line.

Given:
- Slope \( m = -1 \)
- Point \((x_1, y_1) = (4, -6)\)

Substituting these values into the point-slope formula:

\[
y - (-6) = -1(x - 4)
\]

Simplify the equation:

\[
y + 6 = -1(x - 4)
\]

Now, distribute the \(-1\):

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

Subtract 6 from both sides to put it in slope-intercept form (\( y = mx + b \)):

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

\[
y = -x - 2
\]

So, the equation of the line is:

\[
\boxed{y = -x - 2}
\]

Would you like to explore further or have any questions?

### Related Questions
1. How do you convert a point-slope form equation to the standard form of a line?
2. How can you determine the y-intercept given the slope and a point?
3. How would the line equation change if the slope were positive instead?
4. How do you find the x-intercept of the line given its equation?
5. What is the process for graphing this line on a coordinate plane?

**Tip:** Always check if the line equation simplifies correctly by substituting the given point into the final equation.

What is the equation of the line that passes through the point (4, -6) and has a slope of -1?

Learn how to find the equation of a line that passes through the point (4, -6) with a slope of -1. This step-by-step solution covers the point-slope form and simplifies it to slope-intercept form. Suitable for students in Grades 8-10.

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