Answer:
The value of b is 2.
Step-by-step explanation:
Let the equation of line m is,
[tex]y=m_1x+c_1[/tex]
And, line n is,
[tex]y=m_2x+c_2[/tex]
Where, [tex]m_1[/tex] and [tex]m_2[/tex] are the slope of lines m and n respectively.
Since, line m and n are perpendicular,
[tex]m_1\times m_2=-1[/tex]
We have, [tex]m_1=-\frac{1}{2}[/tex],
[tex]\implies -\frac{1}{2}\times m_2=-1[/tex]
[tex]\implies m_2=2[/tex]
Thus, the equation of line n is,
[tex]y=2x+c_2[/tex]
Now, the point (-1,0) is on line n,
[tex]0=2(-1)+c_2\implies c_2=2[/tex]
Hence, the equation of line n is,
[tex]y=2x+2[/tex]
Also, lines m and n intersect at (0,b),
⇒ (0,b) is in both lines m and n,
[tex]\implies b = 2(0) + 2[/tex]
[tex]\implies b =2[/tex]
