SOLUTION: 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 li

Algebra ->  Graphs -> SOLUTION: 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 li      Log On


   

Question 1023521: 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.
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
x and y have formulas with the single variable t.

system%28x=2t%2B3%2Cy=3-3t%29

Solve each of the component or coordinates in terms of t.
system%28t=%28x-3%29%2F2%2Ct=%283-y%29%2F3%29

The two formulas for t show two equal expressions.
%28x-3%29%2F2=%283-y%29%2F3
Appearing to be a linear equation in variables x and y.

3%28x-3%29=2%283-y%29
3x-9=6-2y
highlight%283x%2B2y=15%29--------a more familiar form of equation for this line.