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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.

Find an equation of the line having the given slope and containing the given point: Slope 1/2 through (-4, 2).

Learn how to find the equation of a line with slope 1/2 passing through the point (-4, 2). The solution involves using the point-slope form and converting it to slope-intercept form. Suitable for Grades 8-10.

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