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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.

Guest Nov 23, 2017
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This graphs a line because for every increase in t by 1, x changes by 2 and y changes by -3

 

We only need two points to find a line

 

If t  = 0   we have the point  (3,3)

If t  = 1, we have the point  (5,0)

 

The slope of this line is       -3/2    [ just as we suspected  !!!! ] 

And using (5,0), the equation of the line is

 

y  = (-3/2)(x - 5)

 

y =  (-3/2)x + 15/2

 

To see that this is true.....when  t  = 2,   x = 7    and y  = -3

 

So    

 

y = (-3/2)(7) + 15/2

 

y = -21/2 + 15/2

 

y = -6/2   =    -3    

 

 

cool cool cool

CPhill  Nov 23, 2017
edited by CPhill  Nov 23, 2017

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