Solving for a Cartesian Equation of a Line with Given Vector and Point

[Jeann25]

Homework Statement

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

Homework Equations

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.

 

[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.

 

[TD]

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

<br /> \left\{ \begin{array}{l}<br /> x = 2 - 3t \\ <br /> y = 5 + t \\ <br /> \end{array} \right.<br />

 

[HallsofIvy]

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