`3x - 5y = 3, 3x + 5y = 12` Find the angle theta (in radians and degrees) between the lines

Given:

`3x-5y=3`

`3x+5y=12`

The formula to find the angle between two lines is

`tan(theta)=|(m_2-m_1)/(1+m_1_2)|`

Find the slope of line 1.

`3x-5y=3`

`-5y=-3x+3`

`y=3/5x-3/5`

The slope of line 1 is `m_1=3/5` .

Find the slope of line 2.

`3x+5y=12`

`5y=-3x+12`

`y=-3/5x+12/5`

` `The slope of line 2 is `m_2=-3/5.`

Plug in the slopes into the formula

`tan(theta)=|((m_2-m_1)/(1+m_1m_2))|`

`tan(theta)=|((-3/5)-(3/5))/(1+(3/5)(-3/5))|=15/8`

`theta=arctan(15/8)=61.9^@=1.0808` radians.

The angle between the two lines is 61.9 degrees or 1.0808 radians.