How to convert slope-intercept form into parametric form

Question

$Y = 2x+1$

$Z = 4x$

how to convert to the parametric form ?

Answer 1

Write $y$ and $z$ in terms of $x=t$. You will find $x(t)=t$, $y(t)=2t+1$ and $z(t)=4t$. Then write $$t\mapsto(t,2t+1,4t)$$ that is the parametric form of a line, namely the line passing through the point $P=(0,1,0)$ with direction given by the vector $\vec{v}=\langle1,2,4\rangle$.