Question

Write the parametric equation.

x=3 t-1, y=4-4t
as a function of x in cartesian form.
y=___

Answer 1

To write the parametric equations x = 3t - 1, y = 4 - 4t as a function of x in Cartesian form, solve for t from the x equation and substitute into the y equation. The Cartesian form of the parametric equations is y = (8/3) - (4/3)x.

Step-by-step explanation:

The given parametric equations are x = 3t - 1 and y = 4 - 4t. We want to write y as a function of x in Cartesian form. To do this, we first solve the equation for x to find t: t=(x+1)/3. Then we substitute this expression for t into the equation for y to get y as a function of x.

Upon substitution, we get:

y = 4 - 4((x+1)/3)

After simplifying:

y = 4 - (4/3)x - (4/3)

And combining like terms:

y = (8/3) - (4/3)x

So the Cartesian form of the parametric equations is y = (8/3) - (4/3)x.