# Convert the parametric equations x= 3t, y= t + 7 into a Cartesian equation.

## Question:

Convert the parametric equations x= 3t, y= t + 7 into a Cartesian equation.

## Parametric Curves

A curve given parametrically as {eq}\displaystyle x=f(t), y=g(t) {/eq} is a curve whose points {eq}\displaystyle (x,y), {/eq} are obtained by giving values to the parameter {eq}\displaystyle t. {/eq}

The direction of a parametric curve is given by the direction of increasing {eq}\displaystyle t. {/eq}

Sometimes, to plot a parametric curve, we need the curve in Cartesian form, by eliminating the parameter {eq}\displaystyle t, {/eq}

and obtaining a relationship between {eq}\displaystyle x\text{ and } y. {/eq}

To convert the parametric equation {eq}\displaystyle x=3t, y=t+7, {/eq} into a Cartesian equation,

we will eliminate the parameter t to obtain an equation in terms of x and y.

{eq}\displaystyle x=3t\implies t=\frac{x}{3} \text{ which substituted in the } y-\text{ equation}: \boxed{y=\frac{x}{3}+7 -\text{ is the Cartesian equation}}. {/eq}