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

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to use the following formula to evaluate the angle between lines, such that:

`alpha = tan^(-1)|(f_1'(x) - f'_2(x))/(1 + f_1'(x)*f_2'(x))|`

You need to evaluate `f_1'(x)` and `f_2'(x)` such that:

`f_1'(x) = (3x + 1)' => f_1'(x) = 3`

`f_2'(x) = (-2x - 7)' => f_2'(x) = -2`

`alpha = tan^(-1)|(3 - (-2))/(1 - 6)| => alpha = tan^(-1)|-1|`

`alpha = -tan^(-1) 1 => alpha = -pi/4 => alpha = pi - pi/4 => alpha = 3pi/4`

Hence, evaluating the angle within the given lines yields `alpha = 3pi/4.`

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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.