Linear Algebra question

1. Jan 11, 2007

Jeann25

1. The problem statement, all variables and given/known data

Find a Cartesian equation for the line p + tv, where p=<2,5> and v=<-3,1>

2. Relevant equations

3. The attempt at a solution

I know the vector form will look likse <2,5>+t<-3,1>. But I'm not sure how to use this information to find the equation of the line in y=mx+b form.

2. Jan 11, 2007

Tom1992

Just substitute two points into the line y=mx+b to find m and b. Also, the slope m can be obtained immediately from the direction vector v.

3. Jan 12, 2007

TD

Or, if you write the vector form in components, eliminate t from this system:

$$\left\{ \begin{array}{l} x = 2 - 3t \\ y = 5 + t \\ \end{array} \right.$$

4. Jan 12, 2007

HallsofIvy

Staff Emeritus
Now, solve one equation for t and (I recomment y= 5+ t) and substitute that into the other equation.