Final answer:
To eliminate the parameter in parametric equations and obtain an equation in x and y, we can solve the equations for x and y in terms of the parameter. The curve described by the resulting equation is a straight line with a positive slope, and the positive orientation refers to the direction in which the curve is traced as the parameter increases.
Step-by-step explanation:
To eliminate the parameter and obtain an equation in x and y, we need to solve the given parametric equations for x and y in terms of the parameter. Let's consider an example: x = 2t and y = 3t. To eliminate the parameter t, we can express t in terms of x or y using one of the equations and substitute it into the other equation. In this case, t = x/2. Substituting this value into the equation y = 3t, we get y = 3(x/2), which simplifies to y = 3x/2. Therefore, the equation in x and y is y = 3x/2.
The curve described by this equation is a straight line with a positive slope. It starts at the origin (0,0) and extends indefinitely in both directions. The positive orientation refers to the direction in which the curve is traced as the parameter increases. In this case, as the parameter increases, the curve moves in the positive x and y direction.