Answer
(a) $y=2x+b$
(b) $y=mx+1-2m$
(b) $y=2x-3$
Work Step by Step
(a) In general, we have a specific form of a linear function, that is: $y=mx+b$ (where $m$ stands for the slope and b stands for the $y$-intercept). If $m=2$, the line function will get the following form: $y=2x+b$. Now we can graph several members of this family, for any arbitrary $b$ (Graph (a)).
(b) In this case, we have to use another form of a linear function which formulates like this: $y-y_{1} = m(x-x_{1})$. Inputting the point $f(2)=1$, we will get:
$y-1=m(x-2)$
$y=m(x-2)+1$
And then sketch a graph for any arbitrary $m$. (Graph (b))
(c) To find a function that belongs to both of these functions, we can input the characteristic value of (a) $m=2$ into function (b):
$y=2(x-2)+1$
$y=2x-3$
