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### Problem
Write the equation of a line in **point-slope form** that passes through the point \((-4, -2)\) and has a slope of \(3\).

### Solution
The **point-slope form** of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
where:
- \(m\) is the slope of the line,
- \((x_1, y_1)\) is a point on the line.

Here:
- \(m = 3\),
- \((x_1, y_1) = (-4, -2)\).

Substitute the given values into the formula:
\[
y - (-2) = 3(x - (-4))
\]

Simplify:
\[
y + 2 = 3(x + 4)
\]

This is the **point-slope form** of the equation:
\[
y + 2 = 3(x + 4)
\]

Would you like a detailed explanation of the solution process? Let me know if you have any questions!

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Here are 5 related questions to expand your understanding:
1. How can you rewrite the equation \(y + 2 = 3(x + 4)\) in slope-intercept form?
2. What is the y-intercept of the line in this problem?
3. If another line has a slope of \(-\frac{1}{3}\), how would you write its equation through the same point \((-4, -2)\)?
4. What does the slope of \(3\) tell you about the steepness of the line?
5. How would you graph the line given in point-slope form?

**Tip:** The point-slope form is especially useful when you know one point and the slope but don’t need the y-intercept immediately.

Write an equation in point-slope form of the line that passes through (-4, -2) and has a slope of 3.

Learn how to write the equation of a line in point-slope form. This problem demonstrates finding the equation of a line passing through (-4, -2) with a slope of 3, using the point-slope formula. Perfect for students in Grades 7-10.

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