Write the equation of line passing through (3,-3) & (6,-6)

Answer

To find the equation of the line passing through the points (3, -3) and (6, -6), we can follow these steps:

### Step 1: Identify the coordinates
The coordinates given are:
- Point 1: \( (x_1, y_1) = (3, -3) \)
- Point 2: \( (x_2, y_2) = (6, -6) \)

### Step 2: Write the general equation of a line
The general equation of a line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:
\[ \frac{x - x_1}{x_2 - x_1} = \frac{y - y_1}{y_2 - y_1} \]

### Step 3: Substitute the coordinates into the equation
Substituting the coordinates into the general equation:
\[ \frac{x - 3}{6 - 3} = \frac{y - (-3)}{-6 - (-3)} \]
This simplifies to:
\[ \frac{x - 3}{3} = \frac{y + 3}{-3} \]

### Step 4: Cross-multiply to eliminate the fractions
Cross-multiplying gives:
\[ (x - 3)(-3) = (y + 3)(3) \]

### Step 5: Simplify the equation
Expanding both sides:
\[ -3x + 9 = 3y + 9 \]
Now, subtract 9 from both sides:
\[ -3x + 9 - 9 = 3y + 9 - 9 \]
This simplifies to:
\[ -3x = 3y \]

### Step 6: Rearranging the equation
Dividing both sides by 3 gives:
\[ -x = y \]
Or, rearranging gives:
\[ x + y = 0 \]

### Final Answer
The equation of the line passing through the points (3, -3) and (6, -6) is:
\[ x + y = 0 \]