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: (7, 6) (4, 0)

Answer 1

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

Steps:
1. Compute the slope m = (y2 − y1)/(x2 − x1).
2. Substitute m and one point (x1,y1) into y = mx + b and solve for b.
3. Write the equation y = mx + b.

Apply to your points (7, 6) and (4, 0):
- m = (6 − 0)/(7 − 4) = 6/3 = 2
- Use (4,0): 0 = 2(4) + b → b = −8

So the line is y = 2x − 8. (Check: for x = 7, y = 14 − 8 = 6.)

If you actually need a system of two lines, repeat the same process for the second line (using two exact points from that line).