Question

The acute angle between the lines x – 3y – 6 = 0 and y = 2x + 5 is

Answer 1

Answer:

Step-by-step explanation:

eq. of line x-3y-6=0

3y=x-6

y=1/3 x-6/3

or

y=1/3 x-2

its slope m1=1/3

y=2x+5

slope m2=2

if α is the angle between the lines then

$tan~\alpha =|\frac{m1-m2}{1+m1m2} |=|\frac{\frac{1}{3} -2}{1+1/3\times 2}| =|\frac{1-3\times2}{3+2}| =5/5=1=tan 45\\\alpha =45^\circ$