Question

Find a set of parametric equations for y = -2x + 7, given the parameter t = √(x + 4).

A) x = t² - 4, y = -2(t² - 4) + 7.
B) x = t² + 4, y = -2(t² + 4) + 7.
C) x = t² - 4, y = -2(t² + 4) + 7.
D) x = t² + 4, y = -2(t² - 4) + 7.

Answer 1

The set of parametric equations for y = -2x + 7, given t = √(x + 4), is x = t² - 4 and y = -2(t² - 4) + 7.

Step-by-step explanation:

The given equation is y = -2x + 7.

To find the parametric equations, we are given that t = √(x + 4).

Square both sides of the equation t = √(x + 4) to get t² = x + 4.

Substitute this value of x into the equation y = -2x + 7 to get y = -2(t²-4) + 7.

Therefore, the correct set of parametric equations is x = t² - 4 and y = -2(t² - 4) + 7, which corresponds to option A.