First find the slope:

Using point-slope reasoning with point $(2,7)$, the equation is

Simplifying gives

So the line's $y$-intercept is $11$, which must be true.

First find the slope of the line through $(4,12)$ and $(16,18)$:

Use point-slope reasoning to move from $x=4$ back to $x=0$. That is a change of $-4$ in $x$, so the change in $y$ is

Starting from $y=12$, the height at $x=0$ is

So the roof edge is $10$ feet above the ground when $x=0$.

The point $(0,4)$ means the starting cost is $4$. The line also passes through $(3,13)$, so the hourly rate is the slope:

That gives the linear model $y=3x+4$, where $x$ is the number of hours. For $5$ hours,

So the total cost is \19$.$

First find the slope using the two points:

Then substitute one point into $y=mx+b$. Using $(4,1)$ gives

so

and therefore

So the value of $b$ is $-3$.

A translation left $2$ units means replace $x$ with $x+2$ in the original equation:

Then translate up $3$ units by adding $3$ to the output:

So the translated line has equation $y=4x+4$.