Chapter 1, Problem 51RE

To determine

To find: The parametrization for the curve.

Answer to Problem 51RE

The parametrization is $x=t$ and $y=\frac{5}{3}\left(t+1\right)$ for $t\in \left[2,\infty \right)$ .

Explanation of Solution

Given information:

The given ray with initial point $\left(2,5\right)$ that passes through $\left(-1,0\right)$ .

Calculation:

The slope of the line that passes through points $\left(2,5\right)$ and $\left(-1,0\right)$ is:

  $\begin{array}{c}m=\frac{0-5}{-1-2}\\ =\frac{-5}{-3}\\ =\frac{5}{3}\end{array}$

The slope-point equation of the line is,

  $y=\frac{5}{3}\left(x+1\right)$

One possible way to parameterizecurve of the line is,

  $x=t$ and $y=\frac{5}{3}\left(t+1\right)$

For $t\in \left[2,\infty \right)$ because the ray start with the point $\left(2,5\right)$ .

Therefore, the possible parametrization is $x=t$ and $y=\frac{5}{3}\left(t+1\right)$ for $t\in \left[2,\infty \right)$ .