The equation of a straight line passing through the points `(-5,-6) and (3,10)` is

Options

A. `x-2y =4`
B. `2x-y+4 =0`
C. `2x+y=4`
D. `x-2y+4=0`

Answer

To find the equation of a straight line passing through the points \((-5, -6)\) and \((3, 10)\), we can follow these steps:

### Step 1: Identify the points
Let the points be:
- \( (x_1, y_1) = (-5, -6) \)
- \( (x_2, y_2) = (3, 10) \)

### Step 2: Calculate the slope (m) of the line
The slope \(m\) of the line passing through two points is given by the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the values:
\[ m = \frac{10 - (-6)}{3 - (-5)} = \frac{10 + 6}{3 + 5} = \frac{16}{8} = 2 \]

### Step 3: Use the point-slope form of the equation of a line
The point-slope form of the equation of a line is given by:
\[ y - y_1 = m(x - x_1) \]
Using point \((-5, -6)\) and the slope \(m = 2\):
\[ y - (-6) = 2(x - (-5)) \]
This simplifies to:
\[ y + 6 = 2(x + 5) \]

### Step 4: Expand and simplify the equation
Expanding the equation:
\[ y + 6 = 2x + 10 \]
Now, subtract 6 from both sides:
\[ y = 2x + 10 - 6 \]
This simplifies to:
\[ y = 2x + 4 \]

### Step 5: Rearranging to standard form
To express the equation in standard form \(Ax + By + C = 0\):
\[ 2x - y + 4 = 0 \]

Thus, the equation of the straight line passing through the points \((-5, -6)\) and \((3, 10)\) is:
\[ 2x - y + 4 = 0 \]