How would you find the parametric equations for:
1) a line through $(3,1)$ and $(-5,4)$.
2) a segment joining $(1,1)$ and $(2,3)$.
Can anyone show me the steps of doing it cause the way my textbook shows it, it has gotten me in a loop.
[Math] Parametric equations for given line
calculusparametric
Best Answer
A line will be parameterized by $y\colon x\mapsto ax +b$. For instance, to solve 1), you want $$ \begin{align*} 1 &= a\cdot3 +b \\ 4 &= a\cdot(-5) +b \end{align*} $$ since $(3,1)$ and $(-5,4)$ must be of the form $(x,y(x))$ for the desired line. Solve this system to get the coefficients $a$ and $b$.