Modelling Relationships 2 — Solutions

1. Plot the Graph — Tables and Descriptions

   1. y = 2, 3, 4, 5, 6; gradient = 1, y-intercept = 2 ▶ View Solution
   2. y = 0, 3, 6, 9, 12; gradient = 3, y-intercept = 0 ▶ View Solution
   3. y = −1, 1, 3, 5, 7; gradient = 2, y-intercept = −1 ▶ View Solution
   4. y = 4, 3, 2, 1, 0; gradient = −1, y-intercept = 4 ▶ View Solution

2. Linear or Non-Linear

   1. Non-linear — differences 1, 3, 5 are not constant ▶ View Solution
   2. Linear — constant difference of 2 ▶ View Solution
   3. Linear — constant difference of 2 ▶ View Solution
   4. Non-linear — differences 3, 5, 7 are not constant ▶ View Solution
   5. Linear — constant difference of 0; horizontal line y = 5 ▶ View Solution
   6. Non-linear — differences 1, 7, 19 are not constant ▶ View Solution

3. Reading Values from Rules

   1. y = 23 ▶ View Solution
   2. y = 4 ▶ View Solution
   3. x = 4 ▶ View Solution
   4. x = 5 ▶ View Solution
   5. x = 6 ▶ View Solution
   6. x = −3 ▶ View Solution

4. Gradient and y-intercept

   1. m = 3, c = 4 ▶ View Solution
   2. m = −2, c = 7 ▶ View Solution
   3. m = 1, c = −5 ▶ View Solution
   4. m = ½, c = 3 ▶ View Solution
   5. m = −1, c = 0 ▶ View Solution
   6. m = 0, c = 6 (horizontal line) ▶ View Solution
   7. y = 3x + 4 (m = 3) ▶ View Solution
   8. y = −2x + 7 and y = −x ▶ View Solution

5. Real-World Graphs

   1. Gradient = 8 km/h (speed); distance at 2.5 h = 20 km ▶ View Solution
   2. Cost for 50 texts = $40; 100 texts for a $50 bill ▶ View Solution
   3. T = 8°C at t = 4; T = 0 at t ≈ 6 h 40 min ▶ View Solution
   4. Equal at x = 5; at x = 8 Plan B is cheaper ($44 vs $50) ▶ View Solution
   5. h = 0, 15, 20, 15, 0; non-linear; maximum height = 20 m at t = 2 ▶ View Solution

6. More Substitution into Rules

   1. −3, 9, 21 ▶ View Solution
   2. 16, 8, 0 ▶ View Solution
   3. 0, 5, 10 ▶ View Solution
   4. 12, 6, 0 ▶ View Solution
   5. 10, 12, 14 ▶ View Solution
   6. 3, 9, 15 ▶ View Solution

7. More Find the Rule

   1. y = 4x + 2 ▶ View Solution
   2. y = −2x + 9 ▶ View Solution
   3. y = 3x ▶ View Solution
   4. y = 3x − 1 ▶ View Solution
   5. y = 2x + 5 ▶ View Solution
   6. y = −2x + 100 ▶ View Solution

8. Comparing Two Relationships

   1. Same gradient — parallel lines; they never intersect ▶ View Solution
   2. Both at y = 2 when x = 0; cross at (0, 2) — same y-intercept ▶ View Solution
   3. Equal at x = 4 (y = 17) ▶ View Solution
   4. y = 5x − 3; at x = 4, y = 17 ▶ View Solution

9. Graphing — Tables and Descriptions

   1. y = 8, 6, 4, 2, 0; gradient = −2, y-intercept = 8 ▶ View Solution
   2. y = −4, 0, 4, 8, 12; gradient = 4, y-intercept = −4 ▶ View Solution
   3. y = 2, 2.5, 3, 3.5, 4; gradient = ½, y-intercept = 2 ▶ View Solution
   4. y = 0, 1, 4, 9, 16; non-linear (parabola) ▶ View Solution

10. Interpreting Context Graphs

    1. V = 600 − 75t; half-full at t = 4 hours; empty at t = 8 hours ▶ View Solution
    2. A: S = 25w; B: S = 10w + 100; equal at w ≈ 7 weeks; at w = 10, A has more ($250 vs $200) ▶ View Solution
    3. Initial temp = 20°C; T = 8°C at t = 3 h; reaches −20°C at t = 10 hours ▶ View Solution
    4. D = 80 − 60t; arrives at t = 1 h 20 min; at t = 0.5 h, D = 50 km ▶ View Solution
    5. 70 ice creams for x = 6; zero sales at x ≈ 1.3 h; negative y-values not meaningful ▶ View Solution