Answer:
The value of b is 2.
Step-by-step explanation:
Let the equation of line m is,
![y=m_1x+c_1](https://tex.z-dn.net/?f=y%3Dm_1x%2Bc_1)
And, line n is,
![y=m_2x+c_2](https://tex.z-dn.net/?f=y%3Dm_2x%2Bc_2)
Where,
and
are the slope of lines m and n respectively.
Since, line m and n are perpendicular,
![m_1\times m_2=-1](https://tex.z-dn.net/?f=m_1%5Ctimes%20m_2%3D-1)
We have,
,
![\implies -\frac{1}{2}\times m_2=-1](https://tex.z-dn.net/?f=%5Cimplies%20-%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20m_2%3D-1)
![\implies m_2=2](https://tex.z-dn.net/?f=%5Cimplies%20m_2%3D2)
Thus, the equation of line n is,
![y=2x+c_2](https://tex.z-dn.net/?f=y%3D2x%2Bc_2)
Now, the point (-1,0) is on line n,
![0=2(-1)+c_2\implies c_2=2](https://tex.z-dn.net/?f=0%3D2%28-1%29%2Bc_2%5Cimplies%20c_2%3D2)
Hence, the equation of line n is,
![y=2x+2](https://tex.z-dn.net/?f=y%3D2x%2B2)
Also, lines m and n intersect at (0,b),
⇒ (0,b) is in both lines m and n,
![\implies b = 2(0) + 2](https://tex.z-dn.net/?f=%5Cimplies%20b%20%3D%202%280%29%20%2B%202)
![\implies b =2](https://tex.z-dn.net/?f=%5Cimplies%20b%20%3D2)