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?

Answer 1

If the y‑intercept isn’t clearly readable, you can still write each line in y‑intercept (slope‑intercept) form y = mx + b by finding the slope from two clear points on the line and then solving for b. Steps and tips:

1. Pick two clear points on the line.
- Prefer points that fall exactly on grid intersections (integers) to avoid rounding.
- If you only see an x‑intercept and another point, that’s fine too.

2. Compute the slope m:
- m = (y2 − y1) / (x2 − x1).

3. Find b using one of the points:
- Plug the slope and one point (x1,y1) into b = y1 − m·x1.
- Then write y = m x + b.

4. Repeat for the other line (if you need a system).

5. Check: plug a third visible point into your equation to verify it lies on the line. If the graph is imprecise, report any rounding.

Special cases and shortcuts:
- If you can read the x‑intercept a and you know the slope m, then b = −m·a because 0 = m·a + b.
- If the line is horizontal, m = 0 and y = b (b is the y-value).
- If the line is vertical, it cannot be written as y = mx + b; use x = constant instead.
- If you can’t find any exact grid points, estimate coordinates and keep results in fractions or with suitable rounding.

Examples:
- Points (1,2) and (3,−2): m = (−2−2)/(3−1) = −4/2 = −2. Then b = 2 − (−2)(1) = 4. Equation: y = −2x + 4.
- Points (4,0) (x‑intercept) and (2,3): m = (3−0)/(2−4) = 3/−2 = −3/2. Then b = 3 − (−3/2)(2) = 6. Equation: y = −3/2 x + 6.

If you want, tell me the coordinates of two readable points for each line (or upload the graph) and I’ll derive the equations and produce the system.