Finding $y$-intercept of a parallel line

Question

I have two parallel lines. The equation of the first line is

$$y = -x -3.$$

The distance between the parallel lines is $0.5$. How do I find the $y$-intercept of the second line?

Thanks!

Answer 1

Let $x+y+k=0$ be an equation of the second line.

Thus, $$\frac{|k-3|}{\sqrt{1^2+1^2}}=\frac{1}{2}.$$ Can you end it now?

Answer 2

The slopes of the lines are $-1$. They make $45^\circ$ with the negative $x$-axis. If the distance between the two lines is $\frac{1}{2}$, the difference between their $y$-intercepts should be $\frac{1}{2}\div\cos45^\circ$. There are two possibilities. The second line may have a larger or a smaller $y$-intercept.