The two parallel lines represent the graph of which of the following two pairs of equations?

Question

I got a test question like that and they give me 4 different pair of equations.. I know that if a pair of equations have the same slope those two equations would be parallel. but I would have to find the slope of all 8 equations.. Any one knows a faster way?

(a) x -2y=3 and x -2y=7
(b) x+y=1 and x+y= -2
(c) x+y=1 and z+y= -2
(d) x+y=3 and x-y=5
(e) x-y=7 and x-y=14

I don't need the answer, I need to know HOW to solve it.. THANKS A LOT!!!!!!!!!

Answer 1

rearrange the equation in the form:
y=mx+c
compare the ms

Answer 2

Parallel Lines On A Graph

Answer 3

As all equations are written in the same form
ax+by=c
just find a/b (coefficient of x/coefficient of y) in all cases (or pairs)
wherever a/b is identical the pair of lines are parallel
for eg. in case (a) a/b for line x-2y = 3 is 1/-2 = -2
and for x-2y =1 a/b is again 1/-2 = -2 hence the pair indicated are parallel
in the above cases except for the pair of lines indicated in (d) all the other pairs are parallel
(question (c) is a typo where z should be x)
This is the fastest way of finding out you dont need to rearrange the equation to find slopes. visual finding of a/b is possible

Answer 4

Math method:

The slope of a line can be deducted from the numbers (if any; else it's one) before x and y. If their ratio is equal, the lines are parallel, or they overlap. This rules out one possible answer.

Lines running from lower left to upper right are "ax-by=c", lines from upper left to lower right are "ax+by=c". This will also rule out two answers, and also rule out answer (c) because of "z+y".

You also need to know which particular set matches the lines you're looking at; for this you need to look at an intersection with the X-axis and/or Y-axis. For instance: "x+y=1" will intersect the Y-axis at (0,1) and the X-axis at (1,0). In this particular set of possible answers, it's probably most easy to look at the intersection of the X-axis (thus y equals 0). The first possible answer should have lines crossing the X-axis at x=3 and at x=7.


Guessing method:

Answers (b) and (c) are very similar, except for the letter used for the horizontal axis. I'd look at answer (b) first and see if that matches, this would most likely save some time looking at the other possibilities.
If time is really short, and if I had no time to really look at the answers, I would rule out (c), and guess (b), which does have a better than 25% chance of being the correct answer.

Answer 5

3x + 6y = 18 2x + 5y = 20 to apply graphical approach 2 sparkling up this subject a table of values desires 2 be plotted,i'l decide on extremely some -a million

Answer 6

First option c is retarded cross that out

next find the slope of the graph:
If its 1/2, then ans is a
if its -1, then ans could be b or d
if its 1, then ans is e

next see the y-intercepts:
if they are 1 and -2 then the ans is b
if not then the ans is d

Answer 7

As long as the x and y have the same number in front of them, they will have the same slope. You don't actually need to find the slope, just set it un in slope intercept form, y=mx + b. m is the slope.