Page 145 - Mathematics_F1

Example 6.13

Find the equation of a straight line joining the points A (1, 6) and B (5, 9).
Write the answer in form of ax by c+ += 0.
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Solution
Let ( ,xy 1 ) (1, 6)= and ( ,x 2 y 2 ) (5, 9).=
1
y − y y − y
Using 1 = 2 1 , it follows that,
xx− 1 x − 2 x 1

y − 6 96−
=
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−
x − 1 51
y − 6 = 3
x − 1 4
Cross multiplication gives, 4y − 24 3x= − 3.

Rearranging gives, 3x − 4y + 21 0.=
Therefore, the equation of the line is 3x − 4y + 21 0.=

Example 6.14

Find the equation of a line passing through the points (4, 7) and ( 2,− − 5),
giving your answer in the form ax bx+ = . c

Solution
Let ( ,xy 1 ) (4, 7)= and ( ,x y 2 ) ( 2,= − − 5).
1
2
y − y y − y
From 1 = 2 1 , it follows that,
xx− 1 x − 2 x 1
y − 7 = − 57−
−−
x − 4 = 2 24
7
Mathematics Form One Cross multiplication gives, 1.
y −

x −
4
8
y −
−
7 2x=
1
2x y−=

Therefore, the equation of the line is 2x y−=

138

25/09/2025 15:01:41
Mathematics form 1.indd 138
Mathematics form 1.indd 138 25/09/2025 15:01:41