Which set of parametric equations over the interval 0 ≤ t ≤ 1 defines a line segment with initial point (–5, 3) and terminal point (1, –6)? x(t) = –5 + t; y(t) = 3 – 6t
x(t) = –5 + 3t; y(t) = 1 – 6t
x(t) = –5 + 6t; y(t) = 3 – 9t
x(t) = –5 + 8t; y(t) = 1 – 7t

Given:

A line segment with initial point (–5, 3) and terminal point (1, –6).

To find:

The set of parametric equations over the interval 0 ≤ t ≤ 1 which defines the given line segment.

Solution:

Initial point is (–5, 3). So,

Terminal point is (1, –6).

Check which of the given set of parametric equations satisfy .

Put t=1 in each set of parametric equations.

In option A,

So, option A is incorrect.

In option B,

So, option B is incorrect.

In option C,

Put t=0, in this set of parametric equations.

So, option C is correct.

In option D,

So, option D is incorrect.