Question

Write the parametric equations x = 4 − t, y = 3 − 3t as a function of t in Cartesian form.

A) x = 4 − t, y = 3 − 3t
B) x = 4t − 1, y = 3t − 3
C) x = 4 + t, y = 3 + 3t
D) x = 4t + 1, y = 3t + 3

Answer 1

The Cartesian form of the given parametric equations x = 4 - t and y = 3 - 3t is x = 4t + 1 and y = 3t + 3.

Step-by-step explanation:

The given parametric equations are x = 4 - t and y = 3 - 3t. To convert these equations into Cartesian form, we need to eliminate the parameter t by solving for t in terms of x and y. Let's solve for t in the equation x = 4 - t:

4 - t = x
t = 4 - x

Now, substitute this value of t into the equation y = 3 - 3t:

y = 3 - 3(4 - x)
y = 3 - 12 + 3x
y = -9 + 3x

So, the Cartesian form of the given parametric equations is x = 4 - t and y = -9 + 3x, which is option D) x = 4t + 1, y = 3t + 3.