Question

select the curve represented by the parametric equation indicate the orientation of the curve.x=4-5ty=5+4t

Answer 1

Multiply both sides of the first equation by 4.

`4x=16-20t`

Multiply both sides of the second equation by 5.

`5y=25+20t`

Add the obtained equations.

`4x+5y=41`

Identify the y-intercept of the linear equation. Substitute 0 to the value of x and then solve for y.

`\begin{gathered} 4(0)+5y=41 \\ 5y=41 \\ y=(41)/(5) \\ y=8.2 \end{gathered}`

Thus, the y-intercept is (0,8.2).

Therefore, the graph whose y-intercept is (0,8.2) and whose x-intercept is (10.25,0) is the graph that represents the parametric equations.