Question

The equation of three lines are given below

Answer 1

Answer:

The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3

Step-by-step explanation:

Given as :

The three line equation is

Line 1 : 2 y = 5 x + 6

Line 2 : y = $\frac{2}{5}$ x - 1

Line 3 : 10 x + 4 y = - 6

Now, The standard equation of line is

y = m x + c

where m is the slope of line

And c is the y intercept

So, From Line 1

2 y = 5 x + 6

or , y =  $\frac{5}{2}$ x + $\frac{6}{2}$

I.e y =  $\frac{5}{2}$ x + 3

So,  slope of this line = $m_1$ =  $\frac{5}{2}$

Again , From Line 2

y = $\frac{2}{5}$ x - 1

So, slope of this line =  $m_2$ =  $\frac{2}{5}$

Similarly , From Line 3

10 x + 4 y = - 6

I.e 4 y = - 6 - 10 x

or, y = - $\frac{6}{4}$ -  $\frac{10}{4}$ x

I.e y =  - $\frac{5}{2}$ x  - $\frac{6}{4}$

So, Slope of this line = $m_3$ = - $\frac{5}{2}$

Now, If the lines are parallel , then the slope of the lines are equal

And  If the lines are perpendicular , then the product of the slopes of the lines = - 1

Now, From given lines

$m_2$ × $m_3$ = $\frac{2}{5}$ × ( - $\frac{5}{2}$ )

I.e $m_2$ × $m_3$ = - 1

So, The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3

Hence The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3 Answer