Chapter 1, Problem 50RE

To determine

To find: The parametrization for the curve.

Answer to Problem 50RE

The parametrization is $x=t$ and $y=\frac{5}{3}\left(t+1\right)$ for $t\in \left[-3,4\right]$ .

Explanation of Solution

Given information:The given points are $\left(-3,-2\right)$ and $\left(4,3\right)$ .

Calculation:

Calculate the slope of points $\left(-3,-2\right)$ and $\left(4,3\right)$ .

  $\begin{array}{c}m=\frac{3-\left(-2\right)}{4-\left(-3\right)}\\ =\frac{3+2}{4+3}\\ =\frac{5}{7}\end{array}$

The slope-point equation of the line is,

  $y+2=\frac{1}{7}\left(x+3\right)$

One possible way to parameterize of the line is:

  $x=t$ and $y=\frac{1}{7}\left(t+3\right)-2$

For $t\in \left[-3,4\right]$ , the ray start with the point $\left(-3,-2\right)$ and ends with $\left(4,-1\right)$ .

Therefore, the parametrization is $x=t$ and $y=\frac{1}{7}\left(t+3\right)-2$ for $-3\le t\le 4$ .