Consider the graphed equation shown. What is the equation of the line that passes through (−3, 2) and is parallel to the graphed equation?
 

 
y = x – 1

y = –x – 1

y = –x + 4

y = –x + 2

To solve this, we need to identify the equation of a line that is **parallel** to the given graphed equation and passes through the point \((-3, 2)\).

### Step-by-step approach:
1. **Equation of the given line:**
   The equation of the given line is \( y = -x - 1 \). This is in slope-intercept form \( y = mx + b \), where \( m \) is the slope.

2. **Determine the slope of the line:**
   The slope \( m \) of the given equation \( y = -x - 1 \) is \( -1 \).

3. **Parallel lines have the same slope:**
   A line parallel to the given line will also have a slope of \( -1 \). So, the new equation will have the form \( y = -x + b \), where we need to find \( b \).

4. **Use the point \((-3, 2)\) to find \( b \):**
   Substitute \( x = -3 \) and \( y = 2 \) into the equation \( y = -x + b \) to find \( b \).

   \[
   2 = -(-3) + b
   \]
   \[
   2 = 3 + b
   \]
   \[
   b = 2 - 3 = -1
   \]

5. **Final equation:**
   The equation of the line is \( y = -x - 1 \), which matches **option (2)**.

Thus, the equation of the line is:
\[
y = -x - 1
\]

Would you like further clarification on any step? Here are 5 related questions:

1. What is the general form of a line equation?
2. How do you find the slope between two points?
3. How do perpendicular slopes relate to each other?
4. What happens to the equation of a line if it's shifted vertically?
5. Can parallel lines have different y-intercepts?

**Tip:** Parallel lines always have the same slope, but different y-intercepts.

Consider the graphed equation shown. What is the equation of the line that passes through (−3, 2) and is parallel to the graphed equation? y = x – 1, y = –x – 1, y = –x + 4, y = –x + 2

Find the equation of a line that passes through (-3, 2) and is parallel to the equation y = -x - 1. This problem covers linear equations, slope-intercept form, and parallel line properties. Ideal for students in Grades 8-10.

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