Question

Find the equation of the line which intercepts a length 2 on the positive direction of the x-axis and is inclined at an angle of ${135}^{\circ }$ with the positive direction of y-axis.

Answer 1

$\text{The line passes through the point (2, 0)}\text{Also its inclination to y-axis is}{135}^{\circ }$

$\text{That is, the inclination of the given line}\text{with the x-axis is}{180}^{\circ }-{135}^{\circ }\text{That is, the slope of the given line is}{45}^{\circ }\text{The equation of the line having slope 'm'}\text{and passing through the point}(x_1,y_1)isy-y_1=m(x-x_1)\text{Therefore, the required equation is}y-0=tan{45}^{\circ }(x-2)\Rightarrow y=1\times (x-2)\Rightarrow y=x-2\Rightarrow x-y-2=0$