Question 984536: How would I be able to find the variable "k" when I am given the points (-2,3) and (6, k) and the y-intercept of 4?
Answer by josgarithmetic(39617)   (Show Source):
You can put this solution on YOUR website! ---MISTAKE REMOVED---
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The earlier analysis had a mistake, so here is a different solution maybe with better detail.
Assuming the two points and the given y-intercept are all on one line, then you have one known point, one unknown point, and the y-intercept.
Your points:
(-2,3)
(6,k)
(0,4)
You want to be able to solve for the coordinate, k.
Two of the points, very plainly known, will be used for finding the slope of the line which passes through all three of the listed points.
SLOPE is vertical change divided by horizontal change. This means pick two points (the ones which are known), find their vertical change, find their horizontal change, and compute or evaluate the ratio of these.
Slope,  .
The same slope will apply to any two points. Use the unknown (6,k) with either of the other points and the now known slope, in order to solve for k. Choosing (0,4), then known slope and formula of slope give:
 , for the unknown point being found as (6,7).
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