Answer
(a) $$y=3x+b$$
(b) $$y=3x+6$$
(c)
blue: $y=3x+7$
red: $y=3x+6$
green: $y=3x+5$
Work Step by Step
(a) The equation for the family of lines whose members have slope $m$ is$$y=mx+b.$$In this question $m=3$, so the equation for the family of lines whose members have slope $m=3$ is$$y=3x+b.$$
(b) The point $(-1,3)$ lies on the desired line, so we have$$3=3(-1)+b \quad \Rightarrow \quad b= 6.$$Thus, the equation of the line is$$y=3x+6.$$
