Question

Find the equation of the line perpendicular to the line
x+y+2=0 and passing through the point(-1,0)​

Answer 1

Given :

• Equation of the line perpendicular to the line =x+y+2=0

• Passing points =(-1,0)

To Find :

• The equation of the line passing through given point =?

Formulas :

•If the line passing through (x1, y1 ) we use given formula :

$\red\bigstar\boxed{\sf{(y-y_{1}=m(x-x_{1})}}$

Solution :

Given line : x+y+2=0

For finding the slope of the line we arrange the equation :

$\implies \sf \: x + y + 2 = 0 \\ \\ \implies \sf \: x + y = - 2 \\ \\ \implies \sf \: y + x = - 2 \\ \\ \implies \sf \: y = - x + 2 \\ \\ \implies \boxed{ \sf{slope \: = - 1}}$

If the question wants in perpendicular we use relation:

$\red\bigstar{\boxed{\sf{m_{1}.m_{2}=-1}}}$

Putting slope in this relation :

$\implies \sf \: - 1m = - 1 \\ \\ \implies \boxed{ \sf{slope \: of \: the \: equation \to \: m = 1}}$

Equation of line passing through given point :

$\\ \implies\sf{(y-y_{1}=m(x-x_{1})}$

$\implies \sf \: (y - 0) = 1(x + 1) \\ \\ \implies \sf \: y = x + 1 \\ \\ \implies \sf \: y - x - 1 = 0 \\ \\ \implies \sf \: - x + y - 1 = 0 \\ \\ \implies \sf \: x - y + 1 = 0$

The equation of the line passing through given point is x-y+1=0