Write an equation of the line that passes through the point P and is parallel to the line with the given equation. 
P(-2, -2); x+y=-3

We are asked to find the equation of a line that passes through point \( P(-2, -2) \) and is parallel to the given line \( x + y = -3 \).

### Step 1: Identify the slope of the given line

The given line is written in standard form: 
\[
x + y = -3
\]
To find the slope, we convert this into slope-intercept form, \( y = mx + b \), where \( m \) is the slope. 

Starting with:
\[
x + y = -3
\]
Solve for \( y \):
\[
y = -x - 3
\]

Now, we can see that the slope \( m \) of the given line is \( -1 \).

### Step 2: Use the point-slope form of a line

Since the new line is parallel to the given line, it will have the same slope, \( m = -1 \).

Now, we'll use the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
where \( (x_1, y_1) \) is the given point, and \( m \) is the slope. The point \( P(-2, -2) \) is given, so \( x_1 = -2 \) and \( y_1 = -2 \), and \( m = -1 \).

Substitute the values:
\[
y - (-2) = -1(x - (-2))
\]
Simplify:
\[
y + 2 = -1(x + 2)
\]

### Step 3: Simplify to slope-intercept form

Expand and simplify the equation:
\[
y + 2 = -x - 2
\]
Subtract 2 from both sides:
\[
y = -x - 4
\]

### Final Answer:
The equation of the line that passes through \( P(-2, -2) \) and is parallel to \( x + y = -3 \) is:
\[
y = -x - 4
\]

Do you want more details or have any questions?

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Here are 5 related questions:
1. What is the equation of a line parallel to \( y = 2x + 3 \) that passes through \( (1, 4) \)?
2. How do you find the slope of a line perpendicular to \( x + y = -3 \)?
3. What is the point-slope form of the line passing through \( (-3, 5) \) with slope \( 2 \)?
4. Can you find the equation of a line through \( (0, 0) \) that is parallel to \( 3x - y = 7 \)?
5. How do you find the y-intercept of a line given its slope and a point on the line?

**Tip:** The slope of any line parallel to a given line is always the same as the slope of the original line!

Write an equation of the line that passes through the point P and is parallel to the line with the given equation. P(-2, -2); x+y=-3

Learn how to find the equation of a line that passes through the point (-2, -2) and is parallel to x + y = -3. This step-by-step solution covers key algebraic concepts such as slope-intercept form and point-slope form, and is suitable for students in Grades 8-10.

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