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Let's go through the problem step-by-step.

1. **Point-Slope Form of the Line:**  
   The point-slope form of a line is given by the equation:
   \[
   y - y_1 = m(x - x_1)
   \]
   where \( m \) is the slope and \( (x_1, y_1) \) is a point on the line.

   Given:
   - Slope (\( m \)) = 4
   - Point (\( x_1, y_1 \)) = (-4, 2)

   Plugging these values into the point-slope form:
   \[
   y - 2 = 4(x + 4)
   \]

2. **Simplifying to Slope-Intercept Form:**  
   Now, let's convert the point-slope form into the slope-intercept form (\( y = mx + b \)):

   Start with the equation:
   \[
   y - 2 = 4(x + 4)
   \]

   Expand and simplify:
   \[
   y - 2 = 4x + 16
   \]
   \[
   y = 4x + 16 + 2
   \]
   \[
   y = 4x + 18
   \]

   So, the slope-intercept form of the equation is:
   \[
   y = 4x + 18
   \]

Would you like further details or have any questions about this solution?

Here are five related questions that might help deepen your understanding:
1. What is the significance of the slope in the point-slope form of a line?
2. How would the equation change if the slope were negative?
3. How do you convert from slope-intercept form back to point-slope form?
4. What are the implications of changing the point used in the point-slope form?
5. How can you graph a line using its point-slope form?

**Tip:** Always ensure you distribute and simplify correctly when converting between forms of linear equations.

Write the point-slope form of the line satisfying the given conditions. Slope = 4, passing through (-4, 2). Then use the point-slope form of the equation to write the slope-intercept form of the equation.

Learn how to find the point-slope form of a line with a slope of 4 passing through the point (-4, 2), and convert it to the slope-intercept form. This problem explores key concepts in linear equations and algebra for Grades 8-10 students.

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