find angle between two lines

Question

x+2y=8

x-2y=2

Answer 1

Write the line equation in slope-intercept form y = mx + b, m is slope and b is y-intercept.

x +2y = 8

x +2y -x = 8-x                                 (Subtract x to each side)

2y = -x + 8

y = -(1/2)x + 8/2                              (Divide each side by 2)

y = -(1/2)x +4                                  (Divide 8/2 = 4)

Compared to the slope intercept equation y = mx +b

slope(m₁) = -1/2, and intercept(b₁) = 4

And again the next equation Write the line equation in slope-intercept form y = mx + b, m is slope and b is y-intercept.

x -2y = 2

x -2y +2y = 2 +2y                            (Add 2y to each side)

x = 2 + 2y   

x -2 = 2 +2y -2                                 (Subtract 2 each side)

2y = x -2                                           (Simplify)

y = (1/2)x - 2/2

y = (1/2)x -1                                     (Simplify)

Compared to the slope intercept equation y = mx +b

slope(m₂) = 1/2, and intercept(b₂) = -1

The Angle between two lines 

tan(θ) = (m₁ -m₂)/(1+m₁m₂)

Substitute the value of m₁ & m₂ above equation

tan( θ ) = ((-1/2) - (1/2))/(1+(-1/2)(1/2))

              = (2(-1/2))/(1-1/4)              (LCM of -1/2 -1/2= 1)                    

              = -1/(4-1)/4                        (LCM of 1 -(1/4) = 3/4)

              = -1 (4/3)                                    

              = -4/3                                 (Simplify)

The value of (θ) = tan(-4/3) = -0.025^o.

Comments

tan(θ) = | (m₁ -m₂)/(1+m₁m₂) |.

θ = tan^-1 (4/3) = 53.13^O.

Therefore, the angle between lines (θ) is 53.13^O .