Hello Beth Cohen and Welcome!
To answer the question about your computer running slow: Go to your Applications folder --> Utilities Folder --> Open Disk Utility --> Select your Macintosh HD drive in the left side of the screen --> Make sure the First Aid tab is selected --> Click on Repair Disk Permissions --> After that task as completed, restart your computer. Let us know how this works out.
As for the black lines appearing, go to System Preferences --> Universal Access --> click the seeing tab --> Click the Options button in the Zoom area --> make sure the "Show preview rectangle when zoomed out" is NOT selected --> click done. To be honest, I am not sure if this will fix your problem or not. But let us know if the lines appear after you have repaired disk permissions.
Cheerio
Searay