If perpendicular lines m and n intersect at (0,b) in the standard (x,y) coordinate plane, what is the value of b ? (1) The slope of the line m is \small -\frac{1}{2} (2) The point (-1,0) is on line n.

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]