Chapter 6.3, Problem 11E

Solution

To eliminate: The parameter and identify the graph. Use the graph to support your answer.

The general equation is $y=x-1$ and the graph is shown in figure $\left(1\right)$ .

Given information:

The equations are $x=1+t$ and $y=t$ .

Calculation:

Simplify the equation $x=1+t$ for $t$ .

  $\begin{array}{c}x=1+t\\ x-1=t\end{array}$

Substitute $y$ for $t$ in the above equation.

  $y=x-1$

This is an equation of a line which passes through $\left(0,-1\right)$ and $\left(1,0\right)$ . Its intercepts are validated by the graph obtained from the parametric equations.

  

Figure (1)

Therefore, the general equation is $y=x-1$ and the graph is shown in figure (1).