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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.

In order for this graph to be a line, we need to verify two things: first, that all the points on the graph are on the proposed line and second, that all points on the proposed line are on the graph. Be sure to deal with both.

Logic  Aug 20, 2018
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Hint:

 

Let  x = 2t + 3   and y = 3 - 3t

 

Rearrange both to get t

 

t = (x - 3)/2   and   t = (3 - y)/3

 

Now equate the two expressions for t and rearrange to get y in terms of x.

Alan  Aug 21, 2018

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