Question

Plot three points and draw the line that has the following parametric equations:

x = t
y = -3t + 6
z = t - 3
Show each step of your process.

The faster you can answer the better!

I attached an image of the problem also in case you want to look at that.

Answer 1

y = -3x + 6

y - 6 = -3x

-1/3 y + 2 = x

z = x -3

z = -1/3 y + 2 -3 = -1/3 y - 1

set z = 0

-1/3 y = 1

y = -3

set y = 0

z = - 1

Answer 2

We are given the parametric equations as:

x = t

y = -3t + 6

z = t - 3

Clearly we could find a relationship between x and y as:

y= -3x+6----(1)

since x=t

Also we can find a relationship between x and z as:

z=x-3-----(2)

Now we can write a relationship between y and z as:

from equation (2) we have:

x=z+3 and putting this value of x in equation (1) to obtain:

y=-3(3+z)+6

y= -3z-3

Now we can consider three points as:

When x=1 y=3 z=-2