In y = -3x + 4, -3 is negative, meaning that the line faces down. 4 is positive and is the y-intercept, meaning that it is 4 points above the origin (0, 0). -3 also means that for every 1 point that the x coordinate is moved, the line will go down 3 points. For example, (1, 3) is on the line and so is (2, 6).
