Question

Construct parametric equations describing the graph of the following equation.y = 4x - 3If y = 1-5, find the parametric equation for x,

Answer 1

Let us begin by defining important terms:

A rectangular equation, or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane. For example y=4x+3 is a rectangular equation.

A curve in the plane is said to be parameterized if the set of coordinates on the curve, (x,y) , are represented as functions of a variable t .

x=f(t)

y=g(t)

Given:

The rectangular equation is defined as:

`y\text{ = 4x - 3}`

If y = t -5

The parametric equation for x is obtained by substitution:

`\begin{gathered} t\text{ -5 = 4x - 3} \\ Make\text{ x the subject of formula} \\ 4x\text{ = t - 5 + 3} \\ 4x\text{ = t - 2} \\ Divide\text{ both sides by 4} \\ x\text{ = }(t-2)/(4) \end{gathered}`

Hence, the parametric equation for x is:

`x\text{ = }(t-2)/(4)`