To find the angle between y = 3x+1 and y = -2x-7.
The lines are in the slope intercept form of y = mx+c, where m is the slope and c is the y intercept.
Therefore slopes of the lines are : m1 = 3 and m2 = -2.
Therefore the angle between the lines are given by:
tanA = (m2-m1)/(1+(m1*m2)) = (-2-3)/(1+(-2)(3)) = -5/-5 = 1
A = arc tan1
A = 45 degree .
Therefore , the angle between the lines is 45 degree.
We'll note the angle between the lines as a.
We'll apply the formula:
tan a = |(m1 - m2)/(1+m1*m2)| (1)
m1 and m2 are the slopes of the given lines.
We'll note the lines:
d1:y=3x+1 => m1 = 3
d2:y=-2x-7 => m2 = -2
We'll substitute m1 and m2 into the formula (1):
tan a = |(3+2)/(1-6)|
tan a = |5/-5|
tan a = |-1|
tan a = 1
a = arctan 1 + k*pi
a = pi/4 + k*pi
The angle between lines is of 45 degrees.