# Straight Line Examples

Here you will learn some straight line examples for better understanding of straight line concepts.

Example 1 : Find the equation of lines which passes through the point (3,4) and the sum of intercepts on the axes is 14.

Solution : Let the equation of line be $$x\over a$$ + $$y\over b$$ = 1   …..(i)

This line passes through (3,4), therefore $$3\over a$$ + $$4\over b$$ = 1   …….(ii)

It is given that a + b = 14   $$\implies$$   b = 14 – a in (ii), we get

$$3\over a$$ + $$4\over 14 – a$$ = 1   $$\implies$$   $$a^2$$ – 13a + 42 = 0

$$\implies$$   (a – 7)(a – 6) = 0   $$\implies$$   a = 7, 6

for a = 7, b = 14 – 7 = 7 and for a = 6, b = 14 – 6 = 8

Putting the values of a and b in (i), we get the equations of lines

$$x\over 7$$ + $$y\over 7$$ = 1   and   $$x\over 6$$ + $$y\over 8$$ = 1

Example 2 : If x + 4y – 5 = 0 and 4x + ky + 7 = 0 are two perpendicular lines then k is –

Solution : $$m_1$$ = -$$1\over 4$$   $$m_2$$ = -$$4\over k$$

Two lines are perpendicular if $$m_1 m_2$$ = -1

$$\implies$$   (-$$1\over 4$$)$$\times$$(-$$4\over k$$) = -1   $$\implies$$   k = -1

Example 3 : If the straight line 3x + 4y + 5 – k(x + y + 3) = 0 is parallel to y-axis, then the value of k is –

Solution : A straight line is parallel to y-axis, if its y-coefficient is zero

i.e. 4 – k = 0   i.e.   k = 4

Example 4 : If $$\lambda x^2 – 10xy + 12y^2 + 5x – 16y – 3$$ = 0 represents a pair of straight lines, then $$\lambda$$ is equal to –

Solution : Comparing with $$ax^2+2hxy+by^2+2gx+2fy+c$$ = 0

Here a = $$\lambda$$, b = 12, c = -3, f = -8, g = 5/2, h = -5

Using condition $$abc+2fgh-af^2-bg^2-ch^2$$ = 0, we have

$$\lambda$$(12)(-3) + 2(-8)(5/2)(-5) – $$\lambda$$(64) – 12(25/4) + 3(25) = 0

$$\implies$$   -36$$\lambda$$ + 200 – 64$$\lambda$$ – 75 + 75 = 0

$$\implies$$   100$$\lambda$$ = 200

$$\therefore$$   $$\lambda$$ = 2

Practice these given straight line examples to test your knowledge on concepts of straight lines.