📐 Slope Formula
- slope (m) = RISE / RUN = (y₂−y₁) / (x₂−x₁)
- + slope = goes up hill | − slope = goes downhill
- slope = 0 = flat line | undefined = vertical line
📝 3 Forms of a Line
- Slope-Intercept: y = mx + b (best for graphing!)
- Standard: Ax + By = C
- Point-Slope: y − y₁ = m(x − x₁)
📍 Given 2 Points → Equation
- 1. slope: m = (y₂−y₁)/(x₂−x₁)
- 2. plug in: y−y₁ = m(x−x₁)
- 3. simplify to y = mx + b
- e.g. Points (2,3) and (4,7):
- m = (7−3)/(4−2) = 4/2 = 2
- y−3=2(x−2) → y = 2x − 1
📈 Equation → Find Points
- 1. Make table: x = 0, 1, 2, −1
- 2. Plug each x in, solve for y
- e.g. y = 3x + 2:
- x=0 → y=2 | x=1 → y=5
- x=2 → y=8 | x=−1 → y=−1
- Plot each (x,y) on graph!
🔀 Parallel & Perpendicular
- PARALLEL: SAME slope, diff y-int
- y=2x+1 and y=2x−5 (both m=2)
- PERPENDICULAR: FLIP & CHANGE SIGN
- m=3 → perp. slope = −1/3
- m=2/5 → perp. slope = −5/2
- "Negative reciprocal"
📌 y-intercept & x-intercept (zero)
- Y-INTERCEPT: set x = 0, solve for y → point (0, y). For y=2x+4: y=4 → point (0, 4)
- X-INTERCEPT (zero): set y = 0, solve for x → point (x, 0). For y=2x+4: 0=2x+4 → x=−2 → point (−2, 0)
- On DESMOS: click where line touches each axis to read the exact coordinates!
🔢 Desmos Strategies
3 Ways to Get the Answer!
Strategy 1: Evaluate / Find a Value
- CAPITAL letters to evaluate
- Type M*X + B
- Add sliders M, X, and B
- Set X to your x-value
- Desmos gives you the y-value!
- Use to find any point on line.
Strategy 2: Graph / Visualize
- Type y = 2*x + 3 (lowercase)
- Desmos draws the line instantly!
- Click y-axis crossing = y-intercept
- Click x-axis crossing = x-intercept
- Count rise/run between points
- = verify slope calculation!
Strategy 3: Generate Table
- Type y = 2*x + 3 → click Table
- x: 0,1,2,3 → y: 3,5,7,9
- y increases by 2 each step
- That constant change = SLOPE!
- x=0 row → y=3 = y-intercept!
- Table reveals slope AND intercept!
Remember This!
- In y = mx + b: m = slope (steepness) and b = y-intercept (where line hits y-axis). Memorize this!
- To find y-intercept: set x = 0. To find x-intercept (zero): set y = 0 and solve for x.
- Vertical line: x = 3 (undefined slope) | Horizontal line: y = 3 (slope = 0)