To write an equation in point-slope form, we use the formula:

$y - y_1 = m(x - x_1)$

where:

• $(x_1, y_1)$ is a point on the line,
• $m$ is the slope of the line.

For the given problem:

• The point is $(-6, -3)$, so $x_1 = -6$ and $y_1 = -3$.
• The slope $m$ is $-1$.

Let's substitute these values into the formula:

$y - (-3) = -1(x - (-6))$

Simplify the equation:

$y + 3 = -1(x + 6)$

This is the point-slope form of the equation.

To further simplify, you can expand and rearrange it into slope-intercept form ($y = mx + b$) if needed:

$y + 3 = -x - 6$ $y = -x - 6 - 3$ $y = -x - 9$

So, the line's equation in slope-intercept form is:

$y = -x - 9$

Would you like to see the graph of this equation, or do you have questions about any of the steps?

Related Questions

1. How do you find the slope of a line given two points?
2. What is the difference between point-slope form and slope-intercept form?
3. How can you convert from point-slope form to standard form?
4. Why is point-slope form useful when given a point and a slope?
5. How would the equation change if the slope $m$ were positive?

Tip

When working with point-slope form, remember to keep track of the signs for both the coordinates and the slope to avoid calculation errors.