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:
[tex]y\text{ = 4x - 3}[/tex]
If y = t -5
The parametric equation for x is obtained by substitution:
[tex]\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{ = }\frac{t-2}{4} \end{gathered}[/tex]
Hence, the parametric equation for x is:
[tex]x\text{ = }\frac{t-2}{4}[/tex]
