Mathematics (x)	43	46	48	39	30	60	8	45	40
Physics (y)	54	53	63	30	44	75	20	33	49

(a)(i) and (iii) Scale: On each axis, 2 cm represents 10 marks.
(ii) \(\bar{x} = \frac{43 + 46 + 48 + 39 + 30 + 60 + 8 + 45 + 40}{9} = \frac{359}{9} = 39.89 \approxeq 39.9\)
\(\bar{y} = \frac{54 + 53 + 63 + 30 + 44 + 75 + 20 + 33 + 48}{9} = \frac{421}{9} = 46.78 \approxeq 46.8\)
\((\bar{x}, \bar{y}) = (39.9, 46.8)\)
(b)

\(x\)	\(y\)	\(xy\)	\(x^{2}\)
43	54	2322	1849
46	53	2438	2116
48	63	3024	2304
39	30	1170	1521
30	44	1320	900
60	75	4500	3600
8	20	160	64
45	33	1485	2025
40	49	1960	1600
Total		18379	15979

The equation of the line :
\(y - \bar{y} = m(x - \bar{x})\)
\(m = \frac{\sum {xy} - N(\bar{x})(\bar{y})}{\sum {x^{2}} - N(\bar{x})^{2}}\)
= \(\frac{18379 - 9 \times 39.9 \times 46.8}{15979 - (39.9)^{2}} = \frac{18379 - 16805.88}{15979 - 9 \times (39.9)^{2}}\)
= \(\frac{1573.12}{1650.91} \approxeq 0.95\)
Substituting in the equation, \(y - \bar{y} = m(x - \bar{x})\)
\(y - 46.8 = 0.95(x - 39.9)\)
= \(y = 0.95x + 8.895\)
(c) y = 0.95x + 8.895
when x = 28,
\(y = (0.95 \times 28) + 8.895\)
= \(26.6 + 8.895 \approxeq 35.5 marks\).
For a student who scored 28 in Mathematics, his mark in Physics is 35.5.