Find the distance of the line `2x+y=3` from the point`(-1,\ -3)` in the direction of the line whose slope is 1.

Explanation

Slope `1` imply `tan theta=1`

`implies cos theta=1/sqrt2` and `sin theta =1/sqrt2`

The equation of straight line passing through the point A`(-1,-3)` having slope `1`

`frac{x+1}{1/sqrt2}=frac{y+3}{1/ sqrt2}=r`
where r is the distance of any point B on this line from the point A`(-1,-3)`

Any point B `=(-1+frac{r}{sqrt2},-3+frac{r}{ sqrt2})` is on the line `2x+y=3`

`therefore2(-1+frac{r}{ sqrt2})+(-3+frac{r}{ sqrt2})=3`

`\implies-2- sqrt2r-3+r/ sqrt2=3`

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