A line has a slope of 2 and passes through the origin. What is its equation?

The equation of a line in slope-intercept form is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the slope of the line is 2, which means m = 2. The line passes through the origin, which indicates that the y-intercept b = 0.

Substituting these values into the equation gives:

y = 2x + 0 or simply, y = 2x.

This indicates that for every unit increase in x, y increases by 2 units, confirming the slope of 2, and since the line passes through the origin, there is no constant term added to the equation. Hence, the correct equation of the line is y = 2x.