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

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Homework Help Overview

The problem involves finding a Cartesian equation for a line given in vector form, specifically p + tv, where p=<2,5> and v=<-3,1>. The context is within the subject area of linear algebra or analytic geometry.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss converting the vector form of the line into the slope-intercept form y=mx+b. There are suggestions to substitute points into the equation to find the slope and y-intercept. Others propose eliminating the parameter t by expressing the vector form in component equations.

Discussion Status

The discussion is active with various approaches being explored. Some participants offer guidance on how to derive the slope and y-intercept, while others suggest methods for eliminating the parameter t. There is no explicit consensus on a single method yet.

Contextual Notes

Participants are working within the constraints of the problem statement and are considering different interpretations of how to manipulate the vector form to achieve the desired Cartesian equation.

Jeann25
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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.
 
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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.
 
Or, if you write the vector form in components, eliminate t from this system:

[tex] \left\{ \begin{array}{l}<br /> x = 2 - 3t \\ <br /> y = 5 + t \\ <br /> \end{array} \right.[/tex]
 
Now, solve one equation for t and (I recomment y= 5+ t) and substitute that into the other equation.
 

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