Find an equation of the line that satisfies the given conditions.

Through (−2, 8);  slope −1

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.

Find an equation of the line that satisfies the given conditions. Through (−2, 8); slope −1.

Learn how to find the equation of a line passing through the point (-2, 8) with a slope of -1. This algebraic problem explores key concepts such as point-slope form and slope-intercept form, providing a step-by-step solution. Suitable for students in Grades 8-10.

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