# Find the angle between the lines y=3x+1 and y=-2x-7

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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.**