The document discusses different methods to find the equation of a straight line. It provides examples of finding the equation when given: 1) Two points that the line passes through. 2) A point and the slope of the line. 3) The x-intercept and y-intercept. 4) When the x-intercept and y-intercept are equal. 5) When given the y-intercept and slope. Worked examples are provided for each method.

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2. BY: ASSOCIATE PROFESSOR NADEEM UDDIN
* Equation of straight line passing through two points is
( )2 1
1 1
2 1
y y
y y = x x
x x
−
− −
−
Example-13
Find the equation of straight line which passing through the points(-3,4)
and (5,7).
Solution:
7 4
y 4 {x ( 3)}
5 ( 3)
−
− = − −
− −
3
y 4 (x 3)
5 3
− = +
+
3
y 4 (x 3)
8
− = +
8(y 4) 3(x 3)− = +
8y 32 3x 9− = +
0 3x 9 8y 32= + − +
3x 8y 41 0− + =

3. *Equation of straight line having slope(m) and passing through a
point ( 𝒙 𝟏, 𝒚 𝟏) is
y - y1 = m(x - x1)
Example-14
Find the equation of straight line, which passes through the point(3,7) and its slope
is
2
3
.
Solution:
x 3 and y 7
1 1
2
m
3
formula
y y m(x x )
1 1
2
y 7 (x 3)
3
3(y 7) 2(x 3)
3y 21 2x 6
0 2x 6 3y 21
2x 3y 15 0
= =
=
− = −
− = −
− = −
− = −
= − − +
− + =

4. Example-15
In the following graph, the slope of straight line AB = - 3.Find the equation line
AB.
Solution:
Givenm = - 3 and from graph 𝑥1 = 4 , 𝑦1 = 0
𝑦 − 𝑦1 = 𝑚 (𝑥 − 𝑥1 )
𝑦 − 0 = −3 (𝑥 − 4)
𝑦 = −3 𝑥 + 12
3𝑥 + 𝑦 − 12 = 0

5. *Equation of straight line when x-intercept and y-intercept are given
x y
1
a b
+ =
Example-16
Find the equation of straight line having x-intercept =
2
5
and
y-intercept =
3
4
−
.
Solution:
2
x int ercept a
5
3
y int ercept b
4
formula
x y
1
a b
x y
1
2 3
5 4
5x 4y
1
2 3
15x 8y
1
6
15x 8y 6
15x 8y 6 0
− = =
−
− = =
+ =
+ =
−
− =
−
=
− =
− − =

6. Example-17
The x and y intercepts of a straight line are equal. If the line is passing through
(5, 2), then find the equation of the straight line.
Solution:
Given Let x and y intercepts = k
𝑥
𝑎
+
𝑦
𝑏
= 1
Required equation
𝑥
𝑘
+
𝑦
𝑘
= 1
𝑥 + 𝑦
𝑘
= 1
𝑥 + 𝑦 = 𝑘 … … … 𝑒𝑞(𝑖)
eq (i) passing through (5, 2)
From given x = 5, y = 2 put in eq (i)
5 + 2 = 𝑘
𝑘 = 7
Now put value of k = 7 in eq (i)
𝑥 + 𝑦 = 7

7. Example-18
For the graph, find the equation of line 𝐴𝐵̅̅̅̅.
Solution:
From graph x – intercept = 3 = a
y – intercept = 2 = b
𝑥
𝑎
+
𝑦
𝑏
= 1
𝑥
3
+
𝑦
2
= 1
2𝑥 + 3𝑦
6
= 1
2𝑥 + 3𝑦 = 6

8. *Equation of straight line having y-intercept and a slope is
y = mx + c
Example-19
Find the equation of straight line having slope
5
3
and y-intercept=
2
3
−
.
Solution:
Slope = m =
5
3
y-intercept = c =
2
3
−
Formula
y = mx + c
5 2
y x
3 3
5x 2
y
3 3
5x 2
y
3
3y 5x 2
0 5x 2 3y
5x 3y 2 0
−
= +
= −
−
=
= −
= − −
− − =
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