Construct parametric equations describing the graph of the line passing through the following points.

Question

Construct parametric equations describing the graph of the line passing through the following points.

(−8,2) and (8,−15)

If y=3−t, find the parametric equation for x.

Answer 1

x = (16t-152)/17

when t= 1, y = 3-t = 3-1 = 2

and x = (16-152)/17 = -136/17 = -8 (-8,2)

when t = 18, y = 3-18=-15

and x = (16t-152)/17 = (16(18) - 152)/17 = 136/17 = 8 (8,-15)

the line through the two points have slope = (-15-2)/(8--8) = -17/6

y = -17x/16 + b, find b by plugging in either point

2 = -17(-8)/16 + b

b = 2 - 136/16 = -104/16

y = -17x/16 -104/16 = (17x-104)/16 = 3-t

-17x -104 = 48-16t

-17x = 152 -16t

x = -152/17 + 16t/17

x = (16t-152)/17