what equation passes through the origin and has a slope of 7

It'd probably be best to use the slope intercept form here. 

That is:

y = mx + b

where m = slope

and b = the y intercept

 

So basically all you have to do is put in the slope and the y intercept (which is 0, because it goes through the origin) and your done

 

So you'll end up with

y = (7)x + (0)

or just y = 7x.