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Question 1014394: Suppose you graphed every single point of the form (2t + 3, 3-3t). For example, when t=2, we have 2t + 3 = 7 and 3-3t = -3, so (7,-3) is on the graph. Explain why the graph is a line, and find an equation whose graph is this line.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose you graphed every single point of the form (2t + 3, 3-3t). For example, when t=2, we have 2t + 3 = 7 and 3-3t = -3, so (7,-3) is on the graph. Explain why the graph is a line, and find an equation whose graph is this line.
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And if t = -2,
x = 2(-2)+3 = -1
y = 3-3(-2) = 9
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You now have two points::
slope = (9--3)/(-1-7) = 12/-8 = -3/2
Form is y = mx + b
Solve for "b"::
9 = (-3/2)(-1) = b
b = 15/2
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Equation: y = (-3/2)x + 15/2
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Graph:
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OR
x = 2t+3, so t = (x-3)/2
Since y = 3-3t, y = 3-3[(x-3)/2]
Then y = 3 -(3/2)x +(9/2)
Equation:
y = -(3/2)x + 15/2
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Cheers,
Stan H.
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