Positive Slope m > 0
↗
- Goes UP left to right
- e.g. y = 2x + 1
Negative Slope m < 0
↘
- Goes DOWN left to right
- e.g. y = −2x + 1
Zero Slope m = 0
→
- FLAT horizontal line
- y = b
Undefined Slope
↑
- VERTICAL line
- x = a (not a function!)
Example A: Slope from 2 Points
- Points: (1,3) and (4,9)
- m = (9−3)/(4−1) = 6/3 = 2
- Slope = 2 (goes up!)
- Equation: y−3=2(x−1)
- Simplify: y = 2x + 1
- Check: 2(4)+1=9 ✓
Example B: Slope from Equation
- y = 5x − 3 → slope = 5
- 2x+y=8 → y=−2x+8 → m=−2
- 3x−2y=6 → y=(3/2)x−3 → m=3/2
- KEY: get y ALONE first!
- Number next to x = slope!
Example C: Graph from Equation
- y = 2x + 3:
- 1. Plot y-intercept: (0,3)
- 2. Use slope: up 2, right 1
- 3. New point: (1,5)
- 4. Another: (2,7)
- 5. Draw line through points!
🔢 Desmos Strategies
3 Ways to Get the Answer!
Strategy 1: Evaluate / Find a Value
- Type M*X + B (CAPITALS)
- Add sliders for M and B
- Set X to find specific y-value
- Drag M to see slope change
- Drag B to see y-intercept move
- Great for visualizing m & b!
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 on the graph
- = verify slope calculation!
Strategy 3: Generate Table
- Type y = 2*x + 3 → 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!
- Get the Points from table!
Remember This!
- y = mx + b: m = slope (steepness), b = y-intercept (where line starts on y-axis). DONE!
- To find slope from equation: get y ALONE first, then the number multiplied by x is the slope.
- Bigger |m| = steeper line. m=0 = flat line. Undefined m = vertical line (x = number).