Question

Find the equation of the straight line passing through (-2, 3) and inclined at an angle of ${45}^{\circ }$ with the x-axis.

Answer 1

$\text{Let the required equation of the line be}y-y_1=m(x-x_1)\text{Now,}\text{The line is inclined at an angle of}{45}^{\circ }\text{with x-axis}\therefore m=tan{45}^{\circ }=1\left(x_1{y}_1\right)=(-2,3)\therefore y-y_1=m(x-x_1)\Rightarrow y-3=1\left[\right(x-(-2)\left)\right]\Rightarrow y-3=x+2\Rightarrow y-3=x+2\Rightarrow x-y=-5\therefore \text{Equation of required line is x - y + 5 = 0}$