Question

Write a parametric formula for the line that has xy-equation (y + 2) = 1.52 (x - 1). give a vector parallel to this line. give a vector perpendicular to this line. give a point on this line.

Answer 1

We call our real parameter
`t` and try to save some work by setting
`t=x-1` so


`x=t+1`

and


`y = 1.52 t - 2`

or


`(x,y)=(1, -2) + t(1, 1.52)`

That's enough to answer the question.


`(1, 1.52)` is the parallel vector, often called the direction vector.

To get the perpendicular vector, we swap the coordinates and negate one of them; it doesn't matter which.


`(1.52, -1)` is the perpendicular vector.


`(1, -2)` is a point on the line, given by
`t=0.`