As $x$ increases by $2$, the value of $f(x)$ increases by $4$. So the function rises $2$ units in $f(x)$ for each increase of $1$ in $x$. From $x=5$ to $x=7$, $x$ increases by $2$, so $f(x)$ increases by $4$. Since $f(5)=12$, it follows that $f(7)=16$.

Use the slope formula with the two given points:

So the statement that must be true is that the slope is $-2$.

Substitute $x=4$ into the equation of the line: $y=3(4)+2=12+2=14$. So the point on the path has $y$-coordinate $14$.

The total cost is made of two parts: a one-time fee of $4$ dollars and $6$ dollars for each hour. That means the cost starts at $4$ and increases by $6$ for every $1$ hour, so the equation is $y=6x+4$.

A point $(x,y)$ is on the line if its coordinates satisfy the equation $y=4x-3$. For $(1,1)$, substituting $x=1$ gives $y=4(1)-3=1$, which matches the $y$-value. So $(1,1)$ is on the line.