exam Maths Puzzle Numerical Ability

Find the exact value of:
cos(pi/3)-sin(pi/3)without a calculator

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exam Other Question

Write an expression for the slope of a line passing through the points (0,3) and (x, -9). What value of x will make the fraction equivalent to -2.

Thank you!!!
Melanie sqrt3 sqrt3
----- - -----
sqrt6 -1 sqrt6 + 1

sqrt9x^2 = x + 6

I am having a hard time figuring these out. Can you help?(sqrt means square root)