What is the equation of a line that has a slope of -2 and goes through the origin?

Let's translate the terms - being methodical in that respect usually does 90% of the work.
...Equation of a line: y = m*x + n ; where m is the slope, n is the y intercept. (Bar the special case of x = n.)
...goes through (some point [a,b]): b = m*a + n ; In general, you plug in the given point's values for the equation / locus / curve it should be in.
...origin: The point (0,0).

Following the above, you're just one step away from finding the equation.