To find the equation of a line given a point $(-2, 8)$ and a slope of $-1$, we can use the point-slope form of the equation of a line:

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

where $m$ is the slope, and $(x_1, y_1)$ is the given point.

Given:

• $m = -1$
• $(x_1, y_1) = (-2, 8)$

Substitute these values into the point-slope form:

$y - 8 = -1(x + 2)$

Now simplify the equation:

$y - 8 = -x - 2$

Add 8 to both sides:

$y = -x + 6$

Thus, the equation of the line is:

$y = -x + 6$

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

Here are 5 related questions for further practice:

1. Find the equation of a line passing through $(3, -5)$ with slope $2$.
2. Determine the slope of the line passing through the points $(1, 2)$ and $(4, -1)$.
3. Convert the equation $y = 2x - 7$ to standard form.
4. Find the x-intercept and y-intercept of the line $y = -3x + 9$.
5. Determine if the lines $y = \frac{1}{2}x + 4$ and $y = \frac{1}{2}x - 3$ are parallel.

Tip: The slope tells you how steep a line is. A negative slope means the line decreases as you move to the right.