how do you find direction vectors of a line? (e.g., y=2x-1)

Answer 1

Using your example as the line.

y = 2x - 1

Method 1 (Choosing 2 Points)

Let A (0, -1) and B (1, 1) be two arbitrarily chosen points on the given line.

The directional vector would be the vector that points from A to B.

Vector AB = (1, 1) - (0, -1)

Vector AB = i + 2j

Method 2 (Using Slope)

For a two-dimensional line, recognizing that slope is rise over run or y-component over x-component, you can see the directional vector there as well.

m = 2 / 1

So, y-component is 2 so that's 2j while x-component is 1 so i.

Directional Vector = i + 2j

ANSWER: Directional Vector = i + 2j