Answer
Yes, $f\circ g$ is a line with slope $m_1*m_2$.
Work Step by Step
We are given:
$f(x)=m_1x+b_1$
$g(x)=m_2x+b_2$
We find $f\circ g$:
$f\circ g=f(g(x))=f(m_2x+b_2)=m_1(m_2x+b_2)+b_1=m_1*m_2x+m_1*b_2+b_1$
This represents a line with slope $m_1*m_2$
