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.