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?

Question

anonymous · Answer

Help pls

anonymous · Answer

They have same slope but different y-intercept. Look at the slope and y-intercept

tkhunny · Answer

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.

anonymous · Answer

If both equations have the same slope they are parallel to each other. If one slope is a negative reciprocal of another, they are perpendicular.

anonymous · Answer

lines are parallel if they have the same slopes, but different y intercepts. So I would think that the first thing you would need to do is put your equations in y = mx + b form, where m is the slope. Once you find the slopes and y intercepts of the lines, compare them.