Verified answer

The lines are parallel if their slopes are equal.

When you write each equation in y = mx + b form, the slope is the m: it's the number before the x.

In your examples:

3x-4=y

y-3x=8

can be re-written as:

y = 3x - 4 (slope = 3)

y = 3x + 8 (get this by adding 3x to both sides; slope = 3)

Since 3 equals 3, these lines are ARE parallel.

y=-4x+2

-5=-2y+8x

can be re-written as:

y = 4x + 2 (slope = -4)

and

for the second equation, first subtract 8x from both sides:

-5 - 8x = -2y

Divide by -2 on both sides.

5/2 +(8/2)x = y

5/2 + 4x = y

y = 4x + 5/2 (slope = 4)

Since -4 does not equal 4, the slopes are not equal, and the lines are NOT parallel.

well you should start by puting them in y intercept from (y=ax+b)

so the first one would be:

y=3x-4 and

y=8+3x (add 3x to each side) and so that would be the same as y=3x+8.

these are parallel because they have the same slope. if 2 lines have the same slope they are parallel

the second one would be:

y= -4x+2 and

y=4x+ 5/2 <--thats a fraction (you could either at 5 to each side making it 0=-2y+8x+5 and then ad 2y to each side and divide by 2 on each side or you could start with adding 2y to each side, then ad 5 to each side and then finally dividing by 2 or you could subtract 8x from each side and then divide both sides by -2)

these are not parallel because one has a slope of -4 and the other a slope of 4. so one has a negative correlation and the other a positive.

If they have the same slope then they are parallel. The form of the equation of a line is y=mx+b where m is the slope.

The first pair IS parallel because if you solve the 2nd equation for Y then they both have 3 as a slope.

The 2nd pair is NOT parallel for the same reason. You have to solve the 2nd equation for Y (-8/-2=4). 4 is not equal to -4