Question

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.

x = 3t - 5 y = 5t + 1

Answer 1

(See explanation below for further details).

Explanation:

Let be a parametric curve represented by
`x = 3\cdot t - 5` and
`y = 5\cdot t + 1`, where
`t` is the parametric variable.

The curve is represented graphically with the help of a graphing tool, whose outcome is included in the image attached below. The corresponding rectangular equation is found by eliminating t of each equation.

`t = (x+5)/(3)` and
`t = (y-1)/(5)`

`(x+5)/(3) = (y-1)/(5)`

`5\cdot (x+5) = 3\cdot (y-1)`

`5\cdot x +25 = 3\cdot y - 3`

`5\cdot x -3\cdot y = -28`

The parametric equations represents a linear function (first-order polynomial).