# Thread: Finding a set of Parametric equation

1. ## Finding 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.

2. Originally Posted by vanessa123
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.
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:

$\displaystyle l:\left\{\begin{array}{l}x=2-4t \\y=3 + 6t\end{array}\right.$

3. Originally Posted by earboth
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:

$\displaystyle l:\left\{\begin{array}{l}x=2-4t \\y=3 + 6t\end{array}\right.$
so this is how you do that? and thats the finish equation? ok i guess i see the concept. im gonna have to use this to solve the rest of the section so this is the only example i have. thank you for helping

4. 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.