Qualitative blood test

I had sex on may 12th, used a condom I'm on birth control but was doubling up on them because I was forgetting. Because I got paranoid I went and took a plan b. On June 10th just to put my mind at ease I had a blood test done. It came back the next day as negative. I've been told that being that I had sex a month before the blood test was done that the negative result is accurate. Is this true? It was just a negative result not a quantitative test.