The equation of the straight line passing through the points `(0,-4)` and `(-6,2)` is.................

Answer

To find the equation of the straight line passing through the points \( (0, -4) \) and \( (-6, 2) \), we can follow these steps:

### Step 1: Identify the Points
Let point A be \( (0, -4) \) and point B be \( (-6, 2) \).

### Step 2: Calculate the Slope (m)
The slope \( m \) of the line passing through two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of points A and B:
\[ m = \frac{2 - (-4)}{-6 - 0} = \frac{2 + 4}{-6} = \frac{6}{-6} = -1 \]

### Step 3: Use the Point-Slope Form of the Equation
The point-slope form of the equation of a line is given by:
\[ y - y_1 = m(x - x_1) \]
We can use point A \( (0, -4) \) for \( (x_1, y_1) \) and the slope \( m = -1 \):
\[ y - (-4) = -1(x - 0) \]
This simplifies to:
\[ y + 4 = -x \]

### Step 4: Rearranging to Standard Form
Now, rearranging the equation to standard form:
\[ y + 4 + x = 0 \]
or
\[ x + y + 4 = 0 \]

### Final Answer
Thus, the equation of the straight line passing through the points \( (0, -4) \) and \( (-6, 2) \) is:
\[ x + y + 4 = 0 \]

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