Ahhhh, the Pentax K-1000 - a.k.a the student special. Great reliable camera. I see that you want to blur out the backgrounds. Using a telephoto lens is perfect for that kind of effect. Fortunately for you, you're using an SLR so you can see exactly what kind of depth of field you'll get.
If you've been using a 50mm prime lens, you will notice that the zoom lens does not allow in nearly as much light. Maybe it'll allow in 1/2 to 1/4 the amount of light that a 50mm can. Because of this, you have to be aware of how slow you can hand hold a camera at the various focal lengths that your zoom lens has. Often the slowest shutter speed that one can use to avoid camera shake is 1/focal length, but your mileage may vary.
Along with the lens needing faster shutter speeds to avoid camera shake when not using a tripod, you will also notice that you'll get more subject blur too. As the focal length increases it magnifies the subject causing subtle movement to be more pronounced.
As has been mentioned, your zoom lens probably has a maximum aperture that changes as the focal length increases. This happens because of the physical increase in the lens' length. As the light travels down through the lens it dims. In most cases, the light will dim by as much as 50% or 1 full stop. Your camera's light meter will detect this change and you'll see it in the viewfinder. As you zoom in, the needle in the viewfinder will move. You will then need to adjust your shutter speed to match the needle and the hoop.
I strongly suggest that you go to YouTube.com and watch some videos on depth of field and how to manipulate it. In short, the depth of field is affected by the focal length, focusing distance and aperture. Since focal length and focusing distance is chosen based on the subject, you will almost always use the aperture to increase or decrease your depth of field. If your zoom lens has a longer focal length, you will notice that you can get blurry backgrounds easier with it than say a wide-angle lens.
Take a few rolls and definitely keep a journal with you where you can write down your focal length, shutter speed, aperture and ISO settings.