To find the equation of a line given the slope and a point, we can use the point-slope form of a linear equation:

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

Where:

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

In this case, the slope $m = \frac{1}{2}$ and the point is $(-4, 2)$.

Step-by-step solution:

1. Start with the point-slope form: $y - y_1 = m(x - x_1)$
2. Substitute the given values: $y - 2 = \frac{1}{2}(x + 4)$
3. Distribute the slope: $y - 2 = \frac{1}{2}x + 2$
4. Add 2 to both sides to isolate $y$: $y = \frac{1}{2}x + 4$

So, the equation of the line in slope-intercept form is: $y = \frac{1}{2}x + 4$

Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. How would the equation change if the slope were negative?
2. How can you convert this equation to standard form?
3. What is the interpretation of the y-intercept in this equation?
4. How would the graph of this line look?
5. How would you solve for the x-intercept of this line?

Tip: The slope-intercept form, $y = mx + b$, is useful for quickly identifying both the slope $m$ and the y-intercept $b$ of a line.