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In the coordinate plane, we plot the point $(4t - 4, -2t + 7)$ for every real number $t$ to obtain a graph $\mathcal{G}.$ For example, when $t = 2$, we have $4t - 4 = 4$ and $-2t + 7 = 3$, so the point $(4,3)$ lies on the graph $\mathcal{G}$. 

 

(b) Show that every point on the line $y = -\frac{x}{2} + 5$ lies on the graph $\mathcal{G}.$

 

Hints please

 Mar 31, 2020
 #1
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x =  4t - 4                         y  =  -2t + 7

x + 4  =  4t                       y  -7 =  -2t

[ x + 4] / 4   =  t                [ 7 - y ]  / 2    =  t

 

This  implies  that

 

[ 7 - y ]  / 2   =   [ x + 4 ] / 4          

 

4 [ 7 - y ]  =   2 [ x + 4]

 

7  - y  =   (2/4)  [ x + 4]

 

7 - y =  (1/2) ( x + 4)       multiply through  by   -1

 

y  - 7  = (-1/2( ( x + 4)

 

y   = (-1/2)x  -  2  +  7

 

y =(-1/2) x  + 5

 

 

cool cool cool

 Mar 31, 2020

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