Acute angle between two straight lines

Angle between two straight lines is given by    \[\frac{m-n}{1+mn} \]

where m and n are the slopes of straight  line 1 and line 2 respectively.

case1:    if m*n = -1 then lines are perpendicular

case 2:  if m=n lines are parellel.

case 3. \[m\neq n\neq -1 \]  lines are intersecting.

for examples

y=2x+3  and  y= x+2

here m=2 n=1 

lines are intersecting

y=2x+8  y=-(1/2)x+6

m=2 n=-1/2  here m*n=-1 so lines are perpendicular

Posted on by