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: (-5, 5) (-1, 2)

Answer 1

You can find the slope-intercept form y = mx + b from two exact points on the line. Given (-5, 5) and (-1, 2):

1. Find the slope m:
m = (y2 − y1)/(x2 − x1) = (2 − 5)/(-1 − (−5)) = −3/4.

2. Use one point to solve for b (y-intercept). Using (-1, 2):
2 = (−3/4)(−1) + b → 2 = 3/4 + b → b = 2 − 3/4 = 5/4.

So the line in slope-intercept form is
y = −3/4 x + 5/4.

(You can check with the other point: y = (−3/4)(−5)+5/4 = 15/4+5/4 = 20/4 = 5.)

If you prefer integers: multiply both sides by 4 → 4y = −3x + 5, or 3x + 4y = 5.

If you meant a system of two lines, tell me the second pair of points and I’ll do that one too.