The equation of a line with slope $-\frac{1}{\sqrt{2}}$ and makes an intercept of $2 \sqrt{2}$ units on…
The equation of a line with slope $-\frac{1}{\sqrt{2}}$ and makes an intercept of $2 \sqrt{2}$ units on negative direction of $y$-axis is
$\sqrt{2} y-x+4=0$
$x+\sqrt{2} y+2 \sqrt{2}=0$
$\sqrt{2} y+x+4=0$
$x+\sqrt{2} y-2 \sqrt{2}=0$
Solution
The line passes through point $(0,-2 \sqrt{2})$ and has slope $=\frac{-1}{\sqrt{2}}$ Hence equation of line is
$(\mathrm{y}+2 \sqrt{2})=\frac{-1}{\sqrt{2}}(\mathrm{x}-0) \Rightarrow \mathrm{x}+\sqrt{2} \mathrm{y}+4=0$