How do I write the equation of a line in slope intercept form with the given parametric equations?

Question

x=2t+3

 

y=t-4

Answer 1

Just solve one of them for T, then plug into the other and solve for Y. You can solve either one for T, but I choose the second equation:

 

 Y = T - 4

+4      +4

Y+4 = T

Now plug into the other equation:

X = 2T + 3

X = 2(Y+4) + 3

X = 2Y+8 +3

X = 2Y +11   And now you solve for Y:

-11       -11

X-11 = 2Y

(X-11)/2 = 2Y/2

(X-11)/2 = Y

In proper Y = mX+b form...

Y = (1/2)X - 11/2