I'm assuming the triangle has to be in the first quadrant? Because it's possible to construct a triangle of area zero in the 2nd and 4th quadrants.
Suppose the equation of the line, in slope-intercept form, is
Here, the y-intercept is 3-m (where m < 0), and you can solve for the x-intercept. Once you find the x-intercept, find the area in terms of m, and minimize it.