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

Answer:

(See explanation below for further details).

Step-by-step 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.

$t = \frac{x+5}{3}$ and $t = \frac{y-1}{5}$

$\frac{x+5}{3} = \frac{y-1}{5}$

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

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

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

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