Question

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

Answer 1

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.