Respuesta :
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 = [tex]\frac{2}{5}[/tex] 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 = [tex]\frac{5}{2}[/tex] x + [tex]\frac{6}{2}[/tex]
I.e y = [tex]\frac{5}{2}[/tex] x + 3
So, slope of this line = [tex]m_1[/tex] = [tex]\frac{5}{2}[/tex]
Again , From Line 2
y = [tex]\frac{2}{5}[/tex] x - 1
So, slope of this line = [tex]m_2[/tex] = [tex]\frac{2}{5}[/tex]
Similarly , From Line 3
10 x + 4 y = - 6
I.e 4 y = - 6 - 10 x
or, y = - [tex]\frac{6}{4}[/tex] - [tex]\frac{10}{4}[/tex] x
I.e y = - [tex]\frac{5}{2}[/tex] x - [tex]\frac{6}{4}[/tex]
So, Slope of this line = [tex]m_3[/tex] = - [tex]\frac{5}{2}[/tex]
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
[tex]m_2[/tex] × [tex]m_3[/tex] = [tex]\frac{2}{5}[/tex] × ( - [tex]\frac{5}{2}[/tex] )
I.e [tex]m_2[/tex] × [tex]m_3[/tex] = - 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
