Equation of a Straight Line

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Unit 1

• Equation of a Straight Line

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Revision from S4
(x2 , y2)

• The gradient of a straight line is calculated
  using the formula-
• The gradient can also be calculated using -

y2 - y1
(x1. y1)
x2-x1
o
?
a
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Finding a gradient

• Horizontal lines have zero gradient.
• Vertical lines have undefined gradient.
• Parallel lines have equal gradients.

Find the gradients of the lines connecting the
following points- a) (2 , 7) and (5 , 9) b) (3
, -4) and (-1 , 2) c) (1 , 4) and (3 , 4) d)
(5 , 4) and 5 , -2)
m 2/3
m -2/3
m 0
m is undefined
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Collinear Points
C
B

• A,B,C share a common point but AB and BC have
  different gradients(m1?m2) so they are not
  collinear.
• P,Q,R,S do not share a common point although m1
  m2 so they are not collinear.
• M,N,O have a common point and m1m2 so the y are
  collinear.

A
Q
S
P
R
O
N
M
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Perpendicular Lines

• If 2 lines are perpendicular then the product of
  their gradients will be -1 i.e. m1m2 - 1
• Write down the gradient of the line perpendicular
  to the line with gradient -

m -3/2
m 5/4
m -1/2
m 1/4
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Finding a Midpoint

• To calculate the midpoint of a line you can use
  the formula -

x2,y2
x1,y1
M
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Altitude

• The perpendicular bisector of a line meets it at
  right angles and cuts it in two.
• The altitude of a triangle is a line from one of
  its vertices that is perpendicular to the
  opposite side.

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Median

• The median of a triangle is a line from a vertice
  that cuts the opposite side in two.

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Equation of line through (a,b) with gradient m.
(x,y)
m
y -b
(a,b)
x - a
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Last Slide

• Please complete the worksheet