The problem asks for the equation of a line passing through the point $(-6, -8)$ and having a slope of $\frac{1}{2}$.

We use the point-slope form of a line, which is given by:

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

where:

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

Step-by-step solution:

1. Substitute $x_1 = -6$, $y_1 = -8$, and $m = \frac{1}{2}$ into the formula: $y - (-8) = \frac{1}{2}(x - (-6))$

2. Simplify: $y + 8 = \frac{1}{2}(x + 6)$

3. Distribute the $\frac{1}{2}$: $y + 8 = \frac{1}{2}x + 3$

4. Isolate $y$ to get the equation in slope-intercept form ($y = mx + b$): $y = \frac{1}{2}x + 3 - 8$

5. Simplify further: $y = \frac{1}{2}x - 5$

Final Answer:

The equation of the line is: $y = \frac{1}{2}x - 5$

Would you like me to provide more details or graph this equation for you?

Here are 5 related questions to practice further:

1. How do you convert a line equation from point-slope form to standard form?
2. What is the equation of a line parallel to this one that passes through a different point, such as $(2, 3)$?
3. How do you find the y-intercept of a line given its equation in slope-intercept form?
4. What is the equation of a line perpendicular to this one that passes through the point $(-6, -8)$?
5. How can you determine if a given point lies on this line?

Tip: Always verify your final equation by substituting the given point to ensure it satisfies the equation.