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

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

Where:

• $m$ is the slope,
• $(x_1, y_1)$ is the given point on the line.

Substituting the values:

• $m = -\frac{1}{2}$,
• $x_1 = -8$,
• $y_1 = 4$,

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

Now, simplify:

$y - 4 = -\frac{1}{2}x - 4$

Add 4 to both sides to isolate $y$:

$y = -\frac{1}{2}x$

Thus, the equation of the line is:

$y = -\frac{1}{2}x$

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. What is the point-slope form of a line equation used for?
2. How would the equation change if the slope was positive $\frac{1}{2}$?
3. Can you convert this equation to standard form $Ax + By = C$?
4. How do you graph a line using a point and its slope?
5. What is the slope-intercept form of a line equation?

Tip: The slope tells you how steep the line is and its direction; a negative slope indicates the line falls as it moves from left to right.