1. Year 12 – C1
Straight Line Graphs

2. A θ B D C If two lines are parallel they have equal gradients.
If two lines are perpendicular the product of their gradients is -1.
Proof A θ
B D C
Grad of 1 = AD/DB = tanθ
Grad of 2 =-AD/CD= -1/ tanθ
tanθ x -1/ tanθ = -1

3. 2, -½ 2/3, -3 -8, ¼ 13/5, -5/8 -3/4 because 4/3 x -3/4 = -1
Which of these pairs of gradients apply to pairs of perpendicular lines?
2, -½ /3, , ¼ /5, -5/8
What would the gradient of a line be if it was perpendicular to another line with gradient 4/3?
-3/4 because 4/3 x -3/4 = -1

4. Example Given the points A(1, -1), B(5, 2), P(-1, 10), Q(-1, 3) and
R(-1, -3) show that AB is parallel to QR and that BP is
perpendicular to AB.
Grad AB = Grad QR = -3 – Grad BP =
5 – – 5
= ¾ = ¾ = -4/3
Therefore AB and QR parallel, BP perpendicular to AB.

5. y = mx + c m = gradient c = y intercept
Find the gradients and y intercepts of these lines.
2y = 3x – x + 4y = 2

6. Example A(8, 2) lies on the line x – 2y – 4 = 0.
Find the equation of the straight line parallel to
x – 2y – 4 = 0 that passes through B(6, 6).
b) Find the equation of the line perpendicular to x – 2y – 4 = 0 that passes through B(6, 6).
a) Rearranging equation: y = ½x – Grad = ½
m = y – y ½ = y – y = ½x + 3
x – x x – 6
b) If perpendicular Grad = -2
m = y – y = y – y = -2x + 18
x – x1 x - 6

7. Equation of a line joining 2 points
y – y1 = y2 – y1
x – x1 x2 – x1
Example Find the equation of line passing through (3, -1) and (7, 2)
y = y + 1 = ¾
x – – x - 3
y + 1 = ¾(x – 3) y = ¾ x – 9/4 – 1
y = ¾ x – 5/4

8. Further Example
Find the equation of the perpendicular bisector of the line joining (2, -3) and (6, 5)
Mid point = (2 + 6, ) = (4, 1)
Gradient = = 2
6 – 2
Grad of Perp Bis = - ½
m = y – y1 -1/2 = y – 1 - ½(x – 4) = y - 1
x – x x - 4
y = -1/2 x + 3

9. Exercise Find the equation of the line that:
passes through (-1, -6) with gradient 5
passes through (4, 1) parallel to 2y=x – 3
passes through (-2,9) perpendicular to 2y = x – 3
d) passes through (0,4) and (3, 10)
e) passes through (0,7) and (7,0)
f) passes through (6,-2) and (12, 1)
2. Find the equation of the perpendicular bisector of the line joining the points (4,1) and (2,7)
3. A triangle has vertices at A(0,7) B(9,4) and C(1,0). Find
The equation of the perpendicular from C to AB
The equation of the straight line from A to the mid point of BC.