Question

I calculated a direction (you can call it a vector if you want, but it’s really a slope…) and I want to get an x value from a function given a y value.

Basically, I am trying to draw a line from an x, y value to an x, y value and I have the direction.

Say, given a slope/direction of 1/4 (rise over run), a starting point of 200, and an ending y value of 250, how would I find x?

I know this is really basic highschool algebra, but for some reason I can’t conceptualize it…

Answer 1

If the end points are A(x1,y1) and B(x2,y2), the slope is defined as:

m = ( y2 - y1 ) / ( x2 - x1 )

Since you do have the slope, you need to have at least three coordinates in order to be able to compute the remaining one.

From your question I assume you want to compute y2. Therefore, you need to have x1, y1, and x2.

Example:

m = 1/4
A(1,1)
B(9,y2)
---
y2 = ?

m = ( y2 - y1 ) / ( x2 - x1 ) 
y2 - y1 = m * ( x2 - x1 )
y2 = m * ( x2 - x1 ) + y1
y2 = 1/4 * ( 9 - 1 ) + 1
y2 = 3