Question

Find an equation of the line through the points (2,3,4) and (-1,0,2)

Answer 1

Curious, what class is this for?

Answer 2

We wish for our line to pass through both, so it must be in the direction of the vector formed by the two:$$\mathbf{v}=(2-(-1),3-0,4-2)=(3,3,2)$$So now we have a direction vector; pick either point, let's choose \((-1,0,2)\), and we can quite easily make a vector-valued function that describes a curve passing through these points:$$\mathbf{r}(t)=\mathbf{r}_0+t\mathbf{v}=(-1,0,2)+t(3,3,2)$$

Answer 3

... which can also be written $$\mathbf{r}(t)=(-1+3t,3t,2+2t)=(-1+3t)\mathbf{i}+3t\mathbf{j}+(2+2t)\mathbf{k}$$

Answer 4

@FutureMathProfessor likely a multivariable calculus course, typically late calculus II or early III.

Answer 5

Early 3!

Answer 6

thank you!