Find the acute angle between the lines:
y=2x+4 and y=-3x+6

Question

Find the acute angle between the lines:
y=2x+4 and y=-3x+6

anonymous · Answer

the angle, theta, between lines with known slopes, m1 and m2,  is given by the relation:
$\huge tan\theta=\frac{m_2-m_1}{1+m_1m_2} $

anonymous · Answer

So I would do the inverse tan of that?

anonymous · Answer

do you mind to explain how the formula is arrived at?

anonymous · Answer

yep...

anonymous · Answer

Thanks.

anonymous · Answer

ok... 
do you know about inclination??

anonymous · Answer

rise over run?

anonymous · Answer

no... inclination is an ANGLE a line makes with the positive x axis....

anonymous · Answer

yes, so that is tan-1(rise/run)

anonymous · Answer

if in first quadrant

anonymous · Answer

it doesn't matter if it's in the first quadrant or not....
the inclination is just the angle it makes with the positive x axis at the point where the line intesects the x axis:|dw:1355204236495:dw|

anonymous · Answer

on my calc i was getting negative answers that i had to change around...

anonymous · Answer

so to get the angle between two lines, you're basically subtracting the inclination of the two lines....

anonymous · Answer

oh yeah.... sorry, my bad....
the actual formula is:   $\large tan\theta=|\frac{m_2-m_1}{1+m_2m_1}| $

anonymous · Answer

thankyou!

anonymous · Answer

|dw:1355204493130:dw|
the angle between the two lines is alpha and you can just use angle sum formula for tangent.