Question

The set of parametric equations represents a line. Without eliminating the parameter, find the slope of the line. x = 7 + 2t, y = 5 – 4t II dy/ dx =?

Answer 1

`(dy)/(dx)=-2`

Explanation:

Given a set of parametric equations that represent a line. Find the slope of the line without eliminating the parameter.

`x = 7 + 2t \\ y = 5 - 4t`

Differentiate each equation with respect to t.

`x = 7 + 2t \\\\\Longrightarrow \boxed{ (dx)/(dt)=2}`

`y = 5-4t \\\\\Longrightarrow \boxed{ (dy)/(dt)=-4}`

`\boxed{\left\begin{array}{ccc}\text{\underline{Note:}}\\\\\Big{(dy)/(dx)=(((dy)/(dt) ))/(((dx)/(dt)))} \end{array}\right}`

`(dy)/(dx)=(((dy)/(dt) ))/(((dx)/(dt)))} \\\\\Longrightarrow (dy)/(dx)=(-4)/(2) \\\\\therefore \boxed{\boxed{(dy)/(dx)==-2}}`

Thus, the problem is solved.