Find the equation of a straight line passing through the point (4, 5) and equally inclined to the lines `3x = 4y + 7 and 5y = 12x+6`.

Explanation

let the slope of line be `m_1`

`3x= 4y+7`

`y= (3/4)x +7/4`so m=`3/4` eqn(1)

`y= 12/5x + 6/5` so m=`12/5` eqn(2)

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

`= tan^-1((m_1-3/4)/(1 + 3/4m_1))= tan^-1((m_1-12/5)/(1 + 12/5m_1))`

`= tan^-1((4m_1-3)/(4+3m_1))= tan^-1((5m_1-12)/(5+12m_1))`

`= (4m_1-3)/(1+3m_1)= (5m_1-12)/(5+12m_1)`

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