Final answer:
None of the given parametric forms A, B, C, or D have the slope of -4/3 and y-intercept of 2 that match the original equation 4x+3y-6=0. After analyzing each option, it is evident that neither of them corresponds to the correct slope and intercept of the original line.
Step-by-step explanation:
To determine which parametric form is equivalent to the equation of the line given by 4x+3y-6=0, we first need to express it in slope-intercept form, which is y = mx + b. Solving for y, we get y = -4/3x + 2. This indicates that the slope (m) of the line is -4/3 and the y-intercept (b) is 2.
Next, we analyze each parametric form given:
- A. x=0+3t, y=2+4t
- B. x=0+3t, y=2-4t
- C. x=-2-3t, y=3+4t
- D. x=3-3t, y=2-4t
The correct parametric equations must have the slope of the line when expressing y in terms of x. For instance, if we solve the y parametric form for t in option B, we get t=(y-2)/(-4). Substituting this into the x parametric equation, we have x=0+3((y-2)/(-4)), simplifying to x=-3/4y + 3/2. This means the slope is -3/4, which is not the same as the original line's slope since we are looking for a slope of -4/3.
After performing similar substitutions and simplifications for each option, we find that none of the given parametric forms match the slope of -4/3 and the y-intercept of 2 of the original equation. Thus, none of the options A, B, C, or D is an equivalent parametric form of the equation 4x+3y-6=0. Hence, none of the provided options is correct.