https://file.aiquickdraw.com/mathbot/file/1727809175378udcqb45j.jpg

To solve the problem of finding the equation of a line parallel to \( y = -3x - 5 \) that passes through the point (-2, 4), we can follow these steps:

### Step 1: Identify the slope of the given line
The slope of the line given by \( y = -3x - 5 \) is \( -3 \), since the equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. 

Since the new line is parallel to this line, it will have the same slope. Thus, the slope of the new line is also \( -3 \).

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

In this case:
- \( m = -3 \)
- \( (x_1, y_1) = (-2, 4) \)

Substitute these values into the point-slope form:
\[
y - 4 = -3(x - (-2))
\]
Simplify:
\[
y - 4 = -3(x + 2)
\]

### Step 3: Solve for the unknown number
In the image, the equation is written as:
\[
y - ? = -3(x + 2)
\]
Comparing this with our equation \( y - 4 = -3(x + 2) \), it is clear that the number in the "?" position should be **4**.

Thus, the correct number is 4.

Would you like more details on any of the steps?

Here are 5 questions related to this problem:
1. How do we know that two lines are parallel by looking at their equations?
2. What happens if two lines have the same slope but different y-intercepts?
3. Can we use other forms of a line’s equation to find the same result?
4. What if the problem asked for a line perpendicular to \( y = -3x - 5 \)?
5. How would the equation change if the point were different?

**Tip:** Always check that your equation matches the given condition (in this case, being parallel and passing through the specific point).

Write an equation of the line parallel to y = -3x - 5 and passes through (-2, 4). What number should be in the question mark for the equation y - ? = -3(x + 2)?

Learn how to find the equation of a line parallel to y = -3x - 5 that passes through the point (-2, 4) using point-slope form. This step-by-step guide explains the key concepts of linear equations and parallel lines, suitable for students in Grades 9-10.

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