The equation of a straight line passing through the point (-2,3) and making intercepts of equal length on the axes

I got two solutions. One of which is trivial.
  The distance between (0, 0) and the y-intercept is equal to the distance between (0, 0) and the x-intercept. y - 3 = m(x + 2) The y-intercept is y - 3 = 2m y = 2m + 3 The x-intercept is 0 - 3 = m(x + 2) -3/m = x+ 2 x =-2 - 3/m Set the y-intercept equal to the x-intercept and solve for the slope, m.
 One of these slopes will give you a line that passes through the origin itself. This one you can disregard as trivial.