Question

"Determine whether each pair of lines is parallel, perpendicular, or neither.

Q: 6x=5y+1
-12x+10y=1

(I know the answer is parallel but I need help working it out because I got the answer neither)

Answer 1

first put your equations in y = mx + b form where m is the slope and b is the y intercept.
Then we will compare the slopes and the y intercepts.

6x = 5y + 1
6x - 1 = 5y -- divide both sides by 5
6/5x - 1/5 = y...lets rearrange
y = 6/5x - 1/5
here the slope(m) is 6/5 and the y intercept (b) is -1/5

-12x + 10y = 1 -- add 12x to both sides
10y = 12x + 1 -- divide both sides by 10
y = 12/10x + 1/10 -- reduce
y = 6/5x + 1/10
here the slope(m) is 6/5 and the y intercept(b) is 1/10

Now remember this..
if the slopes are the same, and the y intercepts are different, then it is a parallel line
but if the slopes are the same and the y intercepts are the same, then it would be coincident...same line with infinite solutions.
if the slopes are negative reciprocals of each other....that is if one slope is 2 and the other is 1/2, then the lines will be perpendicular.
if the slopes are totally different...like 2 and 1/8...then it is neither

Answer 2

Thank you so much! I have a huge Algebra test tomorrow and I didn't understand those. I have another but will work out by myself to see if I can get the answer on my own. I appreciate your help you rock :)