Find the equation of the line that passes through points (3,5) and (-6,2). Write the equation in slope intercept form.
A. y= 3x+5
B. y= -6x+2
C. y= -6x+5
D. y= 1/3x+4
The common point between lines y= 2x+5 and y= 1/2 x+6 is (3, 1/2).
A. True
B. False
Are the following two lines parallel?
y= 5x-7
y= 5x+6
A. yes
B. no
Are the following two lines perpendicular?
y= 1/2 x+9
y= 1/2 x+3
A. yes
B. no
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 ⇒ y = ¹/₃ x + 4 [OPTION D]
2) y = 2x + 5 .... (1) 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.
