writing a vector equation?

Question

how do you write a vector equation with a given point (_ , _) and a slope?

Answer 1

let your given point be P(a,b,c...) and your slope be a direction given by a vector V(v,w,x,....). I'm assuming you want a vector equation of a line? You can get to any point on the line by starting at P and moving some distance m (maybe negative) in the direction V. So any point R(r,s,t,...) on the line is given by

R = P + mV, where m is some real number.

For example, in 2 dimensions, the line y = (2/3)x + 1 has a y-intercept at (0,1). Let that be P. The slope 2/3 is the vector (3,2). The point (2, 7/3) is on the line, and the equation

(2, 7/3) = (0,1) + m(3,2) works when m = 2/3. m/√13 is the distance you go along the line from P to R.

Answer 2

y = mx + b

You have everything but b, which is the y intercept.
(2,3); slope 2

3 = 2(2) + b
-1 = b

y = 2x -1 is the equation in slope/intercept form. I'm not sure what a vector equation is.

Answer 3

the point p interprete it as a vector.

then eq for the oine that goes throug p and has a given slope v

p + v(1,0) // in case of dimension 3 y will need two slopes