Question

find the angle between the lines 2x+y+4=0 and y-3x=7​

Answer 1

The angle between the lines 2x+y+4=0 and y-3x=7 is equal to π/4.

M1 - the slope of the line 2x+y+4 = 0 is equal to -2

M2 - the slope of the line y-3x = 7 is equal to 3.

Let the angle between the two lines 2x+y+4=0 and y-3x=7 be equal to x.

Using the formula tan x = |(M1 - M2)/(1+M1×M2)|

=> tan x = |(-2 - 3)/(1-6)|

=> tan x = |(-5)/(-5)|

=> tan x = 1

=> x = π/4

The value of the acute angle between the two lines x-2y+2=0 and x+3y+4=0 is equal to π/4.