The set of parametric equation that defines line segment with point (-5,3) and (1,-6) at the interval 0≤t≤1 is x(t)=-5+6t, y(t)=3-9t.
Option: C.
<u>Step-by-step explanation:</u>
The given t range is 0≤t≤1 which has only two numbers as inputs 0 and 1. That marks the two ends of a line segment.
The given equations are,
x(t)=-5+t, y(t)=3-6t. .......1
x(t)=-5+3t, y(t)=1-6t. .....2
x(t)=-5+6t, y(t)=3-9t. .....3
x(t)=-5+8t, y(t)=1-7t. .....4
Substitute the input 0 and 1 in all the equations to get the point (-5,3) and (1,-6).
All the equations has t as second part that will be result in 0, if multiplied by 0. Only the first part will retain.
From equation 1st and 3rd only has 3 in the first part which will produce 3 as y(t) value. And all the x(t) will produce -5.
So we can further proceed with equations 1 and 3.
Apply input as 1 in both equations,
In equation 1,
x(1)=-5+1, y(1)=3-6(1).
x(1)= -6, y(1)=-3.
(-6,-3) is not the given point.
In equation 3,
x(1)=-5+6(1), y(1)=3-9(1).
x(1)= 1, y(1)= -6.
(1,-6) is the given point in the line segment.
∴x(t)=-5+6t, y(t)=3-9t are the parametric equations.
