SOLUTION: these four equations may look different, But three of them have the same graph. which is different? Explain a. y=3/2x+2 b. 2y+3x=4 c. (y-5)=3/2(x-2) d. 2y-3x=4

Algebra ->  Algebra  -> Linear-equations -> SOLUTION: these four equations may look different, But three of them have the same graph. which is different? Explain a. y=3/2x+2 b. 2y+3x=4 c. (y-5)=3/2(x-2) d. 2y-3x=4      Log On

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Question 174321This question is from textbook algebra 1
: these four equations may look different, But three of them have the same
graph. which is different? Explain
a. y=3/2x+2
b. 2y+3x=4
c. (y-5)=3/2(x-2)
d. 2y-3x=4This question is from textbook algebra 1

Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(16868) About Me  (Show Source):
You can put this solution on YOUR website!
Solve b, c, and d for y. You will note that 3 of the 4 equations have a positive slope and one of them, the different one, has a negative slope.

Answer by jim_thompson5910(28476) About Me  (Show Source):
You can put this solution on YOUR website!
First, let's solve the second equation 2y%2B3x=4 for y


2y%2B3x=4 Start with the second equation.


2y=4-3x Subtract 3x from both sides.


2y=-3x%2B4 Rearrange the terms.


y=%28-3x%2B4%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%28%28-3%29%2F%282%29%29x%2B%284%29%2F%282%29 Break up the fraction.


y=-%283%2F2%29x%2B2 Reduce.


Notice how this equation is NOT equivalent to any other equation (so far at least).

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Now, let's solve the third equation %28y-5%29=%283%2F2%29%28x-2%29 for y


y-5=%283%2F2%29%28x-2%29 Start with the third equation


y-5=%283%2F2%29x%2B%283%2F2%29%28-2%29 Distribute 3%2F2


y-5=%283%2F2%29x-3 Multiply 3%2F2 and -2 to get -3


y=%283%2F2%29x-3%2B5 Add 5 to both sides to isolate y


y=%283%2F2%29x%2B2 Combine like terms -3 and 5 to get 2



So this equation is identical to the first equation in part a)



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Now, let's solve the fourth equation 2y-3x=4 for y


2y-3x=4 Start with the fourth equation.


2y=4%2B3x Add 3x to both sides.


2y=3x%2B4 Rearrange the terms.


y=%283x%2B4%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%28%283%29%2F%282%29%29x%2B%284%29%2F%282%29 Break up the fraction.


y=%283%2F2%29x%2B2 Reduce.



So this equation is identical to the first equation in part a) (and in part c)

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So the only equation that is NOT identical to the equation in part a) is the equation in part b)

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Answer:

The only different equation is 2y%2B3x=4