Find the equation of the line passing through the point (1,3)and makin

1.	Find the equation of the line passing through the point (1,3)and making an angle of 45° withthe line x-3y+4=0
Answer» *Refer to ATTACHMENT for diagram.* $\: \:$ ${\huge{\underline{\sf {\pink{Answer}}}}}$ $\: \:$ $\boxed{ 2x \: + \: y \: - \: 5 \: = \: 0 }$ $\: \:$ ${\huge{\underline{\sf {\pink{Explanation :}}}}}$ $\: \:$ Given : $\: \:$ Line : X - 3y + 4 = 0 $\sf \theta = 45 \degree$ $\: \:$ To Find : $\: \:$ Equation of required line. $\: \:$ SOLUTION : $\: \:$ $\sf \: Slope \: of \: line \: = \frac{ - (coefficient \: of \: x)}{coefficient \: of \: y} \\$ = $\frac{-(-3)}{1} \\$ = 3 $\: \:$ Angle = 45° $\sf \: tan \: \theta = \frac{{m}_{1} - {m}_{2}}{1 + {m}_{1}{m}_{2}} \\$ ↬ $\sf \: tan \: 45° = \frac{{m}_{1} - 3}{1 + {m}_{1} 3} \\$ ↬ $\sf \: 1 = \frac{m - 3}{1 + 3m} \\$ ↬ 1 + 3m = m - 3 ↬ 2M = - 4 ↬ m = -2 $\: \:$ Given point on the line = ( 1 , 3 ) Slope of given line = - 2 $\: \:$ Equation of line : $\: \:$ $\sf \: y - {y}_{1} = m(x - {x}_{1})$ ⇢ $\sf \: y - 3 = -2(x - 1)$ ⇢ $\sf \: y - 3 = -2x + 2$ ⇢ $\sf \: 2x + y - 5 = 0$