Question

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: (-6, 4) (-4, 1)

Answer 1

If you can't read the y‑intercept, use two clear points on the line to find the slope and then solve for b.

Given points (-6, 4) and (-4, 1):

1. Slope m = (y2 − y1) / (x2 − x1) = (1 − 4) / (−4 − (−6)) = (−3) / 2 = −3/2.
2. Use y = mx + b and one point to find b. Using (−6, 4):
4 = (−3/2)(−6) + b = 9 + b → b = 4 − 9 = −5.
3. So the line in slope‑intercept form is y = (−3/2)x − 5.

(You can check with the other point: (−3/2)(−4) − 5 = 6 − 5 = 1, which matches.)