SOLUTION: draw the graph of each of the following equations on the same graph paper a)y=2 b)y=6 c)y=2x-2 d)y=2x-6 do you obtain a parallelogram from these four lines?write down the coor

Algebra ->  Coordinate-system -> SOLUTION: draw the graph of each of the following equations on the same graph paper a)y=2 b)y=6 c)y=2x-2 d)y=2x-6 do you obtain a parallelogram from these four lines?write down the coor      Log On


   

Question 597567: draw the graph of each of the following equations on the same graph paper
a)y=2
b)y=6
c)y=2x-2
d)y=2x-6
do you obtain a parallelogram from these four lines?write down the coordinates of the vertices of the parallelogram
Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--
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Here is the graph of the lines. Read below the graph for the rest of the solution.
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%0D%0A+++++graph%28+600%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+2%2C+6%2C+2x-2%2C+2x-6+%29%0D%0A
a)red line: y=2
b)green line: y=6
c)blue line: y=2x-2
d)purple line: y=2x-6
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The four lines do form a parallelogram. We know that it is a parallelogram because the opposite sides are formed by lines with the same slope: y=2 and y=6 both have a slope of 0, while y=2x-2 and y=2x-6 both have a slope of 2.
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To find the vertices of the parallelogram, find the solution for the two equations that intersect at that point. I'll use the substitution method.
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Find the red-blue vertex:
y=2
y=2x-2
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Substitute 2 for y in the second equation and solve for x.
2=2x-2
2x=4
x=2
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The red-blue vertex is (2,2).
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Find the red-purple vertex:
y=2
y=2x-6
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Substitute 2 for y in the second equation and solve for x.
2=2x-6
2x=8
x=4
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The red-purple vertex is (4,2).
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Find the green-blue vertex:
y=6
y=2x-2
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Substitute 6 for y in the second equation and solve for x.
6=2x-2
2x=8
x=4
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The green-blue vertex is (4,6).
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Find the green-purple vertex:
y=6
y=2x-6
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Substitute 6 for y in the second equation and solve for x.
6=2x-6
2x=12
x=6
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The green-purple vertex is (6,6).
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