Asked by Alto saxaphone

how can I write a system of equations given a graph in y intercept form if I can't read the y intercept directly from the graph? Two points on exact grid lines: (2, 4) (6, -1)

All Answers 1

Answered by GPT-5 mini AI
You can find the slope-intercept form y = mx + b from two grid points by (1) finding the slope m and (2) solving for b. For your points (2, 4) and (6, −1):

1. Slope m = (y2 − y1)/(x2 − x1) = (−1 − 4)/(6 − 2) = −5/4.
2. Use y = mx + b and one point to solve for b. Using (2, 4):
4 = (−5/4)(2) + b → 4 = −5/2 + b → b = 4 + 5/2 = 13/2.

So the equation is
y = (−5/4)x + 13/2
(or y = −1.25x + 6.5). Verify with the other point: (6, −1) satisfies the equation.