Question

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?

Answer 1

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.