Angles from two given lines?

Question

Find the angle from line 2, y = -5x + 1, to line 1, y = 3x. Round to one decimel place.

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Answer 1 · 2018-03-17T07:16:18

Angle between the two lines

#color(brown)(theta_1 - theta_2 = 150.3^@#

Standard form of equation of a line in slope form is

# y = mx + c#

#y = -5x + 1# Eqn (2)

#y = 3x# Eqn (1)

Slope of equation (1) #m_1 = 3#

#tan theta_1 = 3#

#theta_1 = tan ^ -1 (3) = 71.6^@#

Slope of equation (2) #m_2 = -5#

#tan theta_2 = -5#

#theta_2 = tan ^ -1 (-5) = -78.7^@#

Angle between the two lines

#color(purple)(theta_1 - theta_2 = 71.6 - (-78.7) = 150.3^@#