1) gradient of line = Δ y ÷ Δ x = (5 -2) ÷ (3 - (-6)) = ¹/₃
using the point-slope form (y-y₁) = m(x-x₁) using (3,5) (y - 5) = ¹/₃ (x -3) y - 5 = ¹/₃x - 1 ⇒ <span> y = ¹/₃ x + 4 [OPTION D]
</span>2) y = 2x + 5 .... (1) <span> </span>y = ¹/₂ x + 6 .... (2)
by substituting y in (1) for y in (2)
2x + 5 = ¹/₂ x + 6 ³/₂ x = 1 x = ²/₃
by substituting found x (2)
y = ¹/₂ (²/₃) + 6 y = ¹⁹/₃
∴ common point is (²/₃ , ¹⁹/₃) thus answer is FALSE [OPTION B]
3) Yes [OPTION A] This is because the both have a gradient of 5 and if they have the same gradient then that means that the two lines are parallel to each other.
4) No [OPTION B] Two lines are perpendicular if their gradients multiply to give - 1 and as such one is the negative reciprocal of the other. Since both gradients are ¹/₂ then they are actually parallel and not perpendicular.
I think that the 4 sisters get 3 pieces each of the muffins because if you cut it in four pieces it gives one piece to each one of the four sisters and you keep doing it with the other two left muffins.
