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?


  • $\begingroup$ do you mean $$y=-x-3$$? $\endgroup$ – Dr. Sonnhard Graubner Feb 2 '18 at 15:08
  • $\begingroup$ yes, I could of written it that way too $\endgroup$ – Ryand.Johnson Feb 2 '18 at 15:27

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?


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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.