Factor the numerator:

Then

provided that $x\ne 2$. Since the question says the expressions are equivalent for all values of $x$ except one, the equivalent expression is $6$.

Because the two lines intersect at $(2,2)$, that point lies on both graphs. Substitute $x=2$ and $y=2$ into $2x+y=k$:

The value of $k$ is $6$.

Because $f$ is linear, its rate of change is constant. From $x=-1$ to $x=2$, $x$ increases by $3$ while $f(x)$ decreases by $6$, so the slope is $\frac{-6}{3}=-2$. Using the point $(2,5)$, the function can be written as

Now set $f(x)=1$:

So the correct answer is $4$.

Let the total cost of each plan be written in terms of $m$. Plan A costs $25+18m$, and Plan B costs $55+13m$. Since Plan B must cost less than Plan A, set up the inequality

Subtract $13m$ from both sides:

Subtract $25$ from both sides:

Divide by $5$:

which is the same as $m>6$. So the inequality that gives all possible values of $m$ is $m>6$.

Because the relationship is linear, first find the slope using any two points. From $(-1,7)$ to $(2,1)$, the change in $y$ is $1-7=-6$ and the change in $x$ is $2-(-1)=3$, so the slope is $\frac{-6}{3}=-2$. That means the equation has the form $y=-2x+b$. Substitute one point, such as $(2,1)$: $1=-2(2)+b$, so $1=-4+b$ and $b=5$. Therefore the equation is $y=-2x+5$.