Grid Runner Activity
Algebra 1 • Coordinate Geometry Graphing Linear Equations
GRID RUNNER: POINT & SLOPE
Anchor the starting coordinate, navigate the slope vector, and chart the line path.
Name:
Date: Period:
Point-Slope Navigation Protocol Formula: \(m = \frac{\Delta y}{\Delta x} = \frac{\text{Rise}}{\text{Run}}\)
Step 1: Anchor Point
Plot the given coordinate \((x_1, y_1)\). This is your launch point.
Step 2: Follow Slope
Count Rise (\(+\) Up / \(-\) Down), then count Run (\(+\) Right). Plot point 2.
Step 3: Chart Trajectory
Plot 1–2 more points. Draw a straight line with arrows on both ends.
01 Standard Positive Slope
Point \((1, 2)\) • \(m = \frac{2}{3}\)
x y 4 -4 4 -4
1. Direction Check
Rise = • Run =
2. Target Points
Point 2: ( , )
Point 3: ( , )
3. Line Slant
[ ] Up [ ] Down
02 Negative Fractional Slope
Point \((-3, 4)\) • \(m = -\frac{1}{2}\)
x y 4 -4 4 -4
1. Direction Check
Rise = • Run =
2. Target Points
Point 2: ( , )
Point 3: ( , )
3. Line Slant
[ ] Up [ ] Down
03 Integer Slope (Whole Number)
Point \((-2, -3)\) • \(m = 2\)
x y 4 -4 4 -4
1. Fraction Form
Write as fraction:
Rise = • Run =
2. Target Points
Point 2: ( , )
Point 3: ( , )
3. Intercept Check
y-intercept: ( , )
04 Reverse Vector Navigation
Point \((3, -1)\) • \(m = -\frac{4}{3}\)
x y 4 -4 4 -4
1. Reverse Tip
Run out of room? Go Up 4, Left 3 (\(\frac{+4}{-3}\)).
2. Target Points
Forward: ( , )
Backward: ( , )
3. Intercept Check
y-intercept: ( , )
Always extend your line completely across the grid and place arrowheads on both ends!
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Phase 2 • Trajectory Mastery Zero Slopes, Undefined Slopes & Intercept Vectors
SPECIAL CASUALTIES & RADAR INTERCEPT
Radar Grid Operations
05 Zero Slope (\(m = 0\)) Point \((0, 3)\)
x y
Fraction Form
\(m = \frac{0}{1} \rightarrow \frac{\text{Rise 0}}{\text{Run 1}}\)
Orientation
[ ] Horizontal [ ] Vertical
Line Equation
y =
06 Undefined Slope (\(m = \text{undef}\)) Point \((-4, -2)\)
x y
Fraction Form
\(m = \frac{1}{0} \rightarrow \frac{\text{Rise 1}}{\text{Run 0 (Undefined)}}\)
Orientation
[ ] Horizontal [ ] Vertical
Line Equation
x =
Radar Intercept Challenge
Plot both drone vectors. Determine which radar beacon each drone intercepts!
x y 4 -4 4 -4 A (3, 5) B (6, 1) C (1, -4) D (-3, 4)
Drone Alpha Flight Vector Start: \((-5, -1)\) • \(m = \frac{3}{4}\)
Calculated Coordinates:
\((-5, -1) \rightarrow\) ( , ) \(\rightarrow\) ( , )
Target Hit:
[ A ] [ B ] [ C ] [ D ]
Drone Bravo Flight Vector Start: \((4, 5)\) • \(m = -2\)
Calculated Coordinates:
\((4, 5) \rightarrow\) ( , ) \(\rightarrow\) ( , )
Target Hit:
[ A ] [ B ] [ C ] [ D ]
*Tip: Express \(m = -2\) as \(\frac{-2}{1}\) (Down 2, Right 1) or backwards as \(\frac{+2}{-1}\) (Up 2, Left 1). Use a ruler to verify exact intercept.
Flight Controller Debrief (Explain Your Reasoning)
1. Vector Reversal: Why does moving Down 3 & Left 4 \(\left(\frac{-3}{-4}\right)\) produce the exact same line as moving Up 3 & Right 4 \(\left(\frac{+3}{+4}\right)\)?
2. Parallel Flight Paths: If Drone Charlie launches from \((0, -3)\) with the same slope as Drone Alpha \(\left(m = \frac{3}{4}\right)\), will their paths ever collide? Why or why not?
Grid Runner Complete • Check coordinates with your flight commander for final sign-off.
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