Find an equation of the line that satisfies the given conditions.
Through (−4, 8);  slope −1

The equation of a line can be expressed using the **point-slope form**:

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

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

Given:
- The point is \((-4, 8)\),
- The slope is \(m = -1\).

Substitute these values into the point-slope form:

\[
y - 8 = -1(x + 4)
\]

Now, simplify the equation:

\[
y - 8 = -x - 4
\]

Add 8 to both sides:

\[
y = -x + 4
\]

Thus, the equation of the line is:

\[
y = -x + 4
\]

Would you like more details or have any questions?

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Here are 5 related questions you can explore:
1. What is the slope of a line parallel to the one we just found?
2. How would the equation change if the slope were 2 instead of -1?
3. Can you find the y-intercept of the line?
4. What is the distance between the point \((-4, 8)\) and the origin?
5. How do you determine the equation of a line perpendicular to this one?

**Tip:** The **slope-intercept form** of a line is \(y = mx + b\), where \(b\) is the y-intercept!

Find an equation of the line that satisfies the given conditions. Through (−4, 8); slope −1

Learn how to find the equation of a line that passes through the point (-4, 8) with a slope of -1 using the point-slope form and slope-intercept form. This algebra problem is suitable for students in Grades 8-10.

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