Question

how can I find the y intercept of a line if I can't read it directly from the graph because its an improper fraction of out of view? Three points on exact grid lines: (2, 6) (2, -3) (-2, 8)

Answer 1

You find the y‑intercept by getting the equation of the line from two known points and then evaluating at x = 0. Steps:

1. Choose two distinct points (x1,y1) and (x2,y2) that lie on the line (they must have different x’s).
2. Compute the slope m = (y2 − y1)/(x2 − x1).
3. Use b = y1 − m·x1 to get the y‑intercept b (so the line is y = m x + b).

With your three listed points note that (2,6) and (2,−3) have the same x so they would be a vertical line x = 2 (no y‑intercept). So at most two of the three can lie on the same nonvertical line. For the two possible nonvertical pairs:

- Using (2,6) and (−2,8):
m = (8−6)/(−2−2) = 2/(−4) = −1/2.
b = 6 − (−1/2)·2 = 6 + 1 = 7.
So y‑intercept = 7.

- Using (2,−3) and (−2,8):
m = (8−(−3))/(−2−2) = 11/(−4) = −11/4.
b = −3 − (−11/4)·2 = −3 + 11/2 = 5/2.
So y‑intercept = 5/2.

Which of these is the actual line on your graph? Tell me which two points are on the same line (or recheck the coordinates) and I’ll confirm the correct y‑intercept.