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.
