Find the equation of the line through the points (-1,-2) and (-5,2) :

Options

A. a. 2x+y=3
B. b. 3x-2y+7=0
C. c. x+y+3=0
D. d. none of these

Answer

To find the equation of the line that passes through the points (-1, -2) and (-5, 2), we can follow these steps:

### Step 1: Identify the points
Let the points be:
- Point 1 (x1, y1) = (-1, -2)
- Point 2 (x2, y2) = (-5, 2)

### Step 2: Calculate the slope (m) of the line
The formula for the slope (m) of a line through two points is given by:
\[ m = \frac{y2 - y1}{x2 - x1} \]
Substituting the values:
\[ m = \frac{2 - (-2)}{-5 - (-1)} = \frac{2 + 2}{-5 + 1} = \frac{4}{-4} = -1 \]

### Step 3: Use the point-slope form of the equation of a line
The point-slope form of the equation of a line is:
\[ y - y1 = m(x - x1) \]
Substituting the slope and one of the points (let's use (-1, -2)):
\[ y - (-2) = -1(x - (-1)) \]
This simplifies to:
\[ y + 2 = -1(x + 1) \]

### Step 4: Simplify the equation
Distributing the -1:
\[ y + 2 = -x - 1 \]
Now, rearranging the equation to standard form:
\[ y + x + 2 + 1 = 0 \]
\[ x + y + 3 = 0 \]

### Final Equation
The equation of the line through the points (-1, -2) and (-5, 2) is:
\[ x + y + 3 = 0 \]