graphing eqn: y-3x=3, 2y+x=11, 2y-4x=8 form 3 sides of....

[kate45]

ok, so i know i should really know this stuff, but ive gotten really confused on this one problem on my homework

the graphs of the equations y-2x=3 , 2y+x =11, and 2y-4x=8 form three sides of a parallelogram. Complete the parallelogram by writing an equation for the graph that forms the fourth side. Justify your answer.

so ive taken the equations and put them into y=mx + b form and i got
y=2x+3, y= -1/2x + 5.5, and y=2x+4
but when i graph that i get a triangle instead of a paralellogram with one side missing
am i graphing wrong, putting it into y=mx+b wrong, or something competely different?

 

[stapel]

the graphs of the equations y-2x=3 , 2y+x =11, and 2y-4x=8 form three sides of a parallelogram. Complete the parallelogram by writing an equation for the graph that forms the fourth side. Justify your answer.

so ive taken the equations and put them into y=mx + b form and i got y=2x+3, y= -1/2x + 5.5, and y=2x+4

Since the first and third of your lines are clearly parallel, having the same slope, I have no idea how you might have graphed them, that you got them to intersect! :shock:

You might want to start by reviewing how to graph straight lines. It should be noted, by the way, that the graph is not actually necessary. All you need to do is find the slope of the missing side (being the parallel of the currently unpaired line), and find the length of that side (using the Distance Formula and the intersection points of the other three sides). Once you know where the last line must intersect two of the other lines, you can plug-n-chug into any of the formulas for line equations that you've learned, and thus find the fourth equation for the parallelogram. :idea:

If you get stuck, please reply with a clear listing of your steps and reasoning so far. Thank you!

Eliz.