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: (-1, 5) (3, 4)

Answer 1

You can find the slope-intercept form y = mx + b even if you can't read b from the graph by using two known points. With (-1, 5) and (3, 4):

1. Find the slope m:
m = (4 − 5) / (3 − (−1)) = −1 / 4 = −1/4.

2. Find b by substituting one point, say (−1, 5):
5 = (−1/4)(−1) + b → 5 = 1/4 + b → b = 5 − 1/4 = 19/4.

So the line is
y = −(1/4)x + 19/4
(or y = −0.25x + 4.75).

Alternate method (treat m and b as unknowns):
From (−1,5): −1·m + b = 5
From (3,4): 3·m + b = 4
Subtract: 4m = −1 → m = −1/4, then substitute to get b = 19/4.