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To solve this problem, let's first go step by step:

### Step 1: Identify the slope of the line
The equation of the line given is \( y = -4x + 2 \). This is in **slope-intercept form**: 
\[ y = mx + b \]
where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

From the equation \( y = -4x + 2 \), the slope \( m = -4 \).

Since the new line is **parallel** to this line, it will have the **same slope**. Therefore, the slope of the new line is also \( -4 \).

### Step 2: Write the equation in **point-slope form**
The point-slope form of a line is given by:
\[
y - y_1 = m(x - x_1)
\]
where:
- \( (x_1, y_1) \) is a point on the line, and
- \( m \) is the slope.

The problem states that the new line passes through \( (-9, -4) \), so \( x_1 = -9 \) and \( y_1 = -4 \). Using the slope \( m = -4 \), the equation in point-slope form becomes:
\[
y - (-4) = -4(x - (-9))
\]
Simplifying:
\[
y + 4 = -4(x + 9)
\]

### Step 3: Simplify the equation to **slope-intercept form**
Now, distribute the slope \( -4 \) on the right-hand side:
\[
y + 4 = -4x - 36
\]
Subtract 4 from both sides to isolate \( y \):
\[
y = -4x - 40
\]

### Final Answer:
- The equation in **point-slope form** is:
  \[
  y + 4 = -4(x + 9)
  \]
- The equation in **slope-intercept form** is:
  \[
  y = -4x - 40
  \]

Would you like any more details or clarifications?

Here are 5 related questions you can explore:
1. How would the equation change if the line passed through a different point?
2. What happens to the slope if the lines are perpendicular instead of parallel?
3. How do you convert from point-slope form to standard form?
4. How can you find the equation of a line given two points instead of a slope?
5. How does the graph of the line change when the slope increases or decreases?

**Tip:** Always check the slope when dealing with parallel or perpendicular lines; parallel lines share the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (-9, -4) and parallel to the line whose equation is y = -4x + 2. Write an equation for the line in point-slope form.

Learn how to write the equation of a line that is parallel to y = -4x + 2 and passes through the point (-9, -4). This tutorial covers point-slope form and slope-intercept form, suitable for students in grades 9-10.

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