Question

Use the result of Exercise 54 to find parametric equations for the line segments connecting the given pairs of points in the direction indicated.

From $(0,c)$to $(-6,c)$

Short answer

As a function, the parametric equation$x=-6v^{\text{'}}y=e-ef,f\in [0,1]$

Step-by-step solution

Step: 1 Given information

Consider the points $(0,e)$to$(-6,e)$

Calculation

The goal is to determine the parametric equations for the line segment that connects the two points. The line segment formula that connects the two points $(a,b)$to $(c,d)$is as follows,$x=a+(c-a)t,y=b+(d-b)t,t\in [0,1]$.

Here, to find the parametric equations, substitute the given values in the equation of line segment.

Now take the points $(0,e)$to $(-6,e)$

Substituting the values in the equation, $x=a+(c-a)$we get,

$x=0+(-6-0)t${ since } $a=0,b=e,c=-6,d=0$

$$\begin{gathered} x=0+(-6)t \\ x=-6t \end{gathered}$$

Step:3 Further calculation

Now take the points $(0,e)$to $(-6,e).$

Substitute the values in the equation$y=b+(d-b)t$we get,

$y=e+(0-e)t${ since } $a=0,b=e,c=-6,d=0$

$$\begin{gathered} y=e+(-e)t \\ y=e-et \end{gathered}$$

Thus, the parametric equations tor the line segment joining the pair of two points

$(,c),(-6,c)$are$x=-6e,y=e-ef,t\in [0,1]$.