Question

Find the equation of the line making an angle of 135° with the positive x-axis and cutting an intercept 3 from the negative y-axis​

Answer 1

To find:

The equation of the line making an angle of 135° with the positive x-axis and cutting an intercept 3 from the negative y axis .

Calculation:

Slope of the line be m :

$\therefore \: m = \tan( \theta)$

$\implies\: m = \tan( {135}^{ \circ} )$

$\implies\: m = \tan( {180}^{ \circ} - {45}^{ \circ} )$

$\implies\: m = - \tan({45}^{ \circ} )$

$\implies\: m = - 1$

Now , general equation of line, where "c" is the intercept from y axis:

$\therefore \: y = mx + c$

$\implies \: y = ( - 1)x+ ( - 3)$

$\implies \: y = - x - 3$

So, required equation:

$\boxed{ \bold{ \: y = - x - 3}}$