Speed is not constant between linear keyframes

Hello, I am doing an animation where I pull out from a fixed point in a still image, by adding keyframes to both position and scale. The animation is doing what I need it to do with one exception: even though the keyframes are set to linear, the speed between them is not constant. In almost every case the section in between each keyframe starts off slow, then ramps up faster and faster until it hits the next keyframe and then slows to a crawl again. This repeats over and over between all keyframes. I am trying to have a constant speed between the keyframes.  Thanks.