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 $b = 0$.

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!