Me with this question on parametric equations

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.

Step-by-step explanation:

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.

if x decreases by 4 then y increases by 10

step-by-step explanation:

the answer

b. they are parallel and will never intersect.