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To find the equation of a line that passes through the point \((-8, 4)\) and has a slope of \(-\frac{1}{2}\), we can use the **point-slope form** of a line, which is:

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

where:
- \(m\) is the slope,
- \((x_1, y_1)\) is the point the line passes through.

### Step 1: Substitute the given point and slope
Given that the slope is \(m = -\frac{1}{2}\) and the point is \((-8, 4)\), substitute these values into the point-slope form:

\[
y - 4 = -\frac{1}{2}(x + 8)
\]

### Step 2: Simplify the equation
Now, distribute the \(-\frac{1}{2}\) on the right-hand side:

\[
y - 4 = -\frac{1}{2}x - 4
\]

### Step 3: Solve for \(y\) to get the slope-intercept form
Add 4 to both sides to isolate \(y\):

\[
y = -\frac{1}{2}x
\]

Thus, the equation of the line is:

\[
y = -\frac{1}{2}x
\]

This is the equation in **slope-intercept form** \(y = mx + b\), where \(m = -\frac{1}{2}\) and the y-intercept \(b = 0\).

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Would you like more details on any step or have any other questions?

Here are some related questions to explore:
1. What is the point-slope form of the equation for a line passing through \((2, -3)\) with slope 3?
2. How do you convert from point-slope form to slope-intercept form?
3. Can you find the equation of a line passing through \((1, -2)\) and parallel to \(y = \frac{3}{4}x - 1\)?
4. How do you determine if two lines are perpendicular based on their slopes?
5. What is the equation of a vertical line passing through \((-5, 3)\)?

**Tip:** The slope-intercept form, \(y = mx + b\), makes it easy to identify the slope and y-intercept directly!

What is the equation of the line that passes through the point (-8, 4) and has a slope of -1/2?

Learn how to find the equation of a line passing through the point (-8, 4) with a slope of -1/2 using the point-slope and slope-intercept forms. This problem demonstrates key algebraic concepts suitable for students in Grades 8-10.

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