What is the first step to show that two lines are parallel, by looking at the equations of the lines, if they are written in standard form?

You do need the slope. It's not obvious in "Standard Form". Ax + By = C ==> y = -(A/B)x + (C/B) There's your slope to compare. Find -A/B for each. 3x + 2y = 4 ==> Slope = -3/2 6x + 4y = 5 ==> Slope = -6/4 = -3/2 3x + y = 4 ==> Slope = -3 The top two examples COULD be parallel. If the constant is the same, that's a bit sneaky because they are really the SAME line. That's not really parallel.