Question

Rewrite the given parametric equations in Cartesian form:X(t) = 2-1y) = 5+y = 5x+5y = 5x+1

Answer 1

Given that

`\begin{gathered} x(t)=2t-1 \\ y(t)=5t \end{gathered}`

In both cases, we will make t the subject of the formula and equate both equations together

`\begin{gathered} x=2t-1 \\ 2t=x+1 \\ (2t)/(2)=(x+1)/(2) \\ t=(x+1)/(2)\ldots\ldots\ldots\ldots\ldots(1) \end{gathered}`
`\begin{gathered} y=5t \\ t=(y)/(5)\ldots\ldots\ldots\ldots\ldots(2) \end{gathered}`

To get the cartesian form, equate equation (1) and (2) together

`\begin{gathered} \frac{x+1_{}}{2}=(y)/(5) \\ by\text{ cross multiplying, we will have} \\ 2y=5(x+1)_{} \\ 2y=5x+5 \\ \text{divide all through by 2 we will have} \\ (2y)/(2)=(5x)/(2)+(5)/(2) \\ y=(5)/(2)x+(5)/(2) \end{gathered}`

Hence,

The correct answer is OPTION C