💡 The GED Drag-and-Drop Format
The GED shows a graph of a line and asks you to drag the correct values (like p, r, and 0) into boxes to complete the equation y = ___x + ___. You must read the slope from the graph's rise and run labels, and identify the y-intercept from the labeled point. This lesson teaches exactly that!
How steep the line is.
Positive m → line goes up left to right ↗
Negative m → line goes down ↘
m = rise ÷ run
Where the line crosses the y-axis (where x = 0).
If the line passes through (0, p), then b = p.
If it passes through the origin, b = 0.
| Equation | Slope (m) | Y-intercept (b) |
|---|---|---|
| y = 2x + 3 | 2 | 3 |
| y = −x + 5 | −1 | 5 |
| y = (p/r)x + 0 | p/r | 0 (origin) |
Slope (m) = Rise ÷ Run
Rise = vertical change (up = positive, down = negative)
Run = horizontal change (right = positive, left = negative)
On the GED graph, the rise and run are often labeled directly with letters like s (side/run) and r (rise), or with arrows showing the vertical and horizontal distances.
Choose points where the line crosses grid intersections — easy to read exactly.
How many units up or down from the first point to the second? Up = positive.
How many units right or left from the first point to the second? Right = positive.
Write as a fraction if needed. Keep signs!
Y-intercept: The line passes through (0, p) — so b = p... but wait! The graph shows the line going THROUGH the origin with a rise bracket labeled and s on the side. Let's analyze carefully.
p = the rise (vertical distance)
r = the run (horizontal distance)
s = an extra label on the side
Y-intercept (0, p) is labeled on the graph
→ Slope = p/r | Y-intercept = p... but (0,p) IS the y-intercept!
So m = p/r → numerator box = p, denominator box = r
| Token | Where It Goes | Why |
|---|---|---|
| p | Numerator of slope | p = the vertical rise of the line |
| r | Denominator of slope | r = the horizontal run of the line |
| 0 | Y-intercept box (+___) | Line crosses y-axis at origin (0,0) |
| s | NOT used | s labels the side/slant — not part of the equation |
Slope = rise ÷ run. The rise is labeled p and run is labeled r on the graph.
The y-intercept is where the line crosses the y-axis. Look at where x = 0 on the graph.
The GED graph labels the rise and run with letters. Rise goes in the numerator, run goes in the denominator.
Look for the labeled point on the y-axis. If it's (0, p), then b = p. If it's at the origin, b = 0.
The GED provides more options than needed. Here, "s" is the label on the slant side of the right triangle — it's NOT used in the equation. Don't be distracted by extra labels!
If the line goes UP from left to right → positive slope. If it goes DOWN → negative slope. Line k goes up → slope is positive (p/r).
| Component | Value | Where from Graph |
|---|---|---|
| Slope (m) | p/r | Rise=p, Run=r labeled on right triangle |
| Y-intercept (b) | 0 | Line passes through origin |
| Equation | y = (p/r)x + 0 | Complete slope-intercept form |