How to find the acute angle between 2 equations?

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Can someone please explain to me how to do question 18? Thanks!

1 Answer
Dec 7, 2017

pi/4.

Explanation:

Let the given lines be l_1 : y=2x+4, and, l_2 : y=-3x+6.

Let m_1, and, m_2 be their respective slopes.

Clearly, m_1=2, and, m_2=-3.

If alpha=/_(l_1,l_2) in [0,pi/2], then, we have,

tanalpha=|(m_1-m_2)/(1+m_1m_2)|,

=|(2-(-3))/(1+2(-3))|,

:. tanalpha=|5/-5|,

rArr alpha=arc tan 1=pi/4.