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? In other words, what is the y intercept? Two points on exact grid lines: (-6, 4) (-4, 1)

Answer 1

You can find the y‑intercept b from two points by first finding the slope, then plugging one point into y = mx + b.

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

1. Slope m = (1 − 4)/(-4 − (−6)) = −3/2.
2. Use y = mx + b with one point, e.g. (-6,4): 4 = (−3/2)(−6) + b → 4 = 9 + b → b = −5.

So the line in slope–intercept form is y = (−3/2)x − 5. (Equivalently 3x + 2y = −10.)