Question

find two different sets of parametric equations for the rectangular equation. (enter your answer in a list as [x = f(t), y = f(t)], [x = f(t), y = f(t)].)y = 9x − 8

Answer 1

Two sets of parametric equations for the rectangular equation y = 9x - 8: x = t, y = 9t - 8; and x = t + 1, y = 9(t + 1) - 8.

Step-by-step explanation:

One set of parametric equations for the rectangular equation y = 9x - 8 can be:

• x = t
• y = 9t - 8

Another set of parametric equations for the same rectangular equation can be:

• x = t + 1
• y = 9(t + 1) - 8

Both sets of equations will generate the same points on the graph as the original equation y = 9x - 8. The parameter t represents a parameter that can take on any value.

Answer 2

Two sets of parametric equations for the given rectangular equation are [x = t, y = 9t - 8] and [x = t + 1, y = 9(t + 1) - 8], providing a representation of the same line with different parameter values.

Step-by-step explanation:

To find two different sets of parametric equations for the rectangular equation y = 9x − 8, we can express x and y in terms of a parameter t. A simple approach is to let x = t, which naturally leads to y = 9t - 8, hereby giving us one set of parametric equations. Another approach is to manipulate the parameter, for instance, by setting x = t + 1, which changes y accordingly to y = 9(t + 1) - 8.

So the two sets of parametric equations could be:

1. [x = t, y = 9t - 8]
2. [x = t + 1, y = 9(t + 1) - 8]

Both sets represent the same line in the Cartesian plane, but they trace the line with different parameter values for t.