The equation of the line passing through (1,2) and perpendicular to `x+y+1=0` is

Options

A. `y-x+1=0`
B. `y-x-1=0`
C. `y-x+2=0`
D. `y-x-2=0`

Answer

To find the equation of the line passing through the point (1, 2) and perpendicular to the line given by the equation \(x + y + 1 = 0\), we can follow these steps:

### Step 1: Find the slope of the given line
The equation of the line is in the form \(Ax + By + C = 0\). For the line \(x + y + 1 = 0\), we can rewrite it in slope-intercept form \(y = mx + b\).

1. Rearranging the equation:
\[ y = -x - 1 \]
Here, the slope \(m\) of the given line is \(-1\).