1. Problem: Complete the tables and plot the points for each given rule. 2. For (a) $y = x + 2$, substitute each $x$: - $x=0 \Rightarrow y=0+2=2$ - $x=1 \Rightarrow y=1+2=3$ - $x=2 \Rightarrow y=2+2=4$ - $x=3 \Rightarrow y=3+2=5$ - $x=4 \Rightarrow y=4+2=6$ - $x=5 \Rightarrow y=5+2=7$ Completed table: $x$: 0 1 2 3 4 5 $y$: 2 3 4 5 6 7 3. For (b) $q = p - 1$, compute $q$: - $p=1 \Rightarrow q=0$ - $p=2 \Rightarrow q=1$ - $p=4 \Rightarrow q=3$ - $p=5 \Rightarrow q=4$ - $p=6 \Rightarrow q=5$ - $p=7 \Rightarrow q=6$ Completed table: $p$: 1 2 4 5 6 7 $q$: 0 1 3 4 5 6 4. For (c) $n = m - 1$, compute $n$: - $m=1 \Rightarrow n=0$ - $m=2 \Rightarrow n=1$ - $m=3 \Rightarrow n=2$ - $m=4 \Rightarrow n=3$ - $m=6 \Rightarrow n=5$ - $m=8 \Rightarrow n=7$ Completed table: $m$: 1 2 3 4 6 8 $n$: 0 1 2 3 5 7 5. For (d) $c = \frac{d}{2} - 1$, compute $c$: - $d=0 \Rightarrow c=0/2-1=-1$ - $d=2 \Rightarrow c=2/2-1=1-1=0$ - $d=4 \Rightarrow c=4/2-1=2-1=1$ - $d=6 \Rightarrow c=6/2-1=3-1=2$ - $d=7 \Rightarrow c=7/2-1=3.5-1=2.5$ - $d=8 \Rightarrow c=8/2-1=4-1=3$ Completed table: $d$: 0 2 4 6 7 8 $c$: -1 0 1 2 2.5 3 6. Exercise 4: Number of hours (t): 2, 3, 4, 5, 7, 10 Kilometres covered (k): 160, 240, 320, 500, 950, 1200 7. (a) Find constant speed $v$ using $v = \frac{\Delta k}{\Delta t}$ between points with constant rate. Check from 2 to 3 hours: $$v = \frac{240 - 160}{3 - 2} = \frac{80}{1} = 80$$ km/h From 3 to 4 hours: $$v = \frac{320 - 240}{4 - 3} = 80$$ km/h consistent From 4 to 5 hours: $$v = \frac{500 - 320}{5 - 4} = 180$$ km/h not consistent Since speeds vary, speed is NOT constant but roughly $80$ km/h early and then increases. 8. (c) i) After 5 hours, kilometres: 500 (given) ii) After 18 hours, assuming early speed 80 km/h extrapolated approx: $$k = 80 \times 18 = 1440$$ km iii) Time $t$ to cover 640 km assuming constant speed 80 km/h: $$t = \frac{640}{80} = 8 \text{ hours}$$ iv) Time for 280 km: $$t = \frac{280}{80} = 3.5 \text{ hours}$$ 9. (d) If Moshe drives all day (say 24 hours - 1 hour break = 23 hours): $$k = 80 \times 23 = 1840$$ km 10. Exercise 4.2: Milk (L): 3, 5, 6, 7, 8, 9 Prices: 12, 20, ?, ?, ?, ? Find price per litre: Between 3 L and 5 L: $$\text{price per litre} = \frac{20 - 12}{5-3} = \frac{8}{2} = 4$$ per litre Complete prices: - 6 L: $4 \times 6 = 24$ - 7 L: $4 \times 7 = 28$ - 8 L: $4 \times 8 = 32$ - 9 L: $4 \times 9 = 36$ 11. (c) Find litres with R50: $$\text{litres} = \frac{50}{4} = 12.5 \approx 13 \text{ litres}$$ 12. (d) Cost of 10 litres: $$10 \times 4 = 40$$ 13. (e) Cost of 30 litres: $$30 \times 4 = 120$$ --- Final answers: see above tables and calculations.