Find a set of parametric equation for the line passing through the points (2,3) and (6,-3).

this is an even number in my book and there are no examples in this section on how to find a parametric equation using two points.

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- Dec 9th 2009, 07:25 AMvanessa123Finding a set of Parametric equation
Find a set of parametric equation for the line passing through the points (2,3) and (6,-3).

this is an even number in my book and there are no examples in this section on how to find a parametric equation using two points. - Dec 9th 2009, 08:00 AMearboth
1. The line in question passes through (2, 3) (Of course, you can use the other point too)

2. The direction of the line is given by (2, 3) - (6, -3) = (-4, 6)

3. The equation of the line is:

$\displaystyle (x, y) = (2, 3) + t \cdot (-4, 6)$

4. Separate the varaibles:

$\displaystyle l:\left\{\begin{array}{l}x=2-4t \\y=3 + 6t\end{array}\right.$ - Dec 9th 2009, 08:39 AMvanessa123
- Dec 9th 2009, 05:37 PMNOX Andrew
An alternative to the method submitted by earboth follows.

Find the equation of the line. Considering the information given, use the point-slope form of the equation of a line and solve for $\displaystyle y$.

$\displaystyle y = -\frac{3}{2}x + 6$

Use $\displaystyle t$ as the parameter and let $\displaystyle x = t$ to produce the first parametric equation.

$\displaystyle x = t$

Substitute $\displaystyle x = t$ in the slope-intercept form of the equation of the line to produce the second parametric equation.

$\displaystyle y = -\frac{3}{2}t + 6$

In case it isn't clear, $\displaystyle x = t$ and $\displaystyle y = -\frac{3}{2}t + 6$ are a set of parametric equation for the line passing through the points (2,3) and (6,-3).

It's as easy as finding the equation of a line y in terms of x and substituting t for x.