Hey! Please help if you can.

Trey needs to rent a car for one day. The rental company offers two plans. Both plans involve paying a fixed amount and then paying an additional charge per mile driven. For each plan, the cost of driving the car, y dollars, is a function of the number of miles traveled. The graph shows the car rental cost for Plan A. Plan B offers a fixed payment of $30 plus 25¢ per mile.

a.
Write an algebraic equation to represent the function for plan B.

b.
Graph the linear function for plan B on the same coordinate plan as Plan A.

c.
Use a verbal description to compare the two functions. Then describe a scenario that would benefit Trey to rent the car using Plan A. Then describe a scenario that would benefit Try using Plan B.

d.
Describe a situation where either rental plan results in the same total cost.

As the problem states, we have two plans: Plan A and Plan B. In this question, we will use Plan B to write an equation from the graph. We can write an equation having two points. Thus, from the graph, we know the two points:

[tex]P_{1}(0,20) \ and \ P_{2}=(140,70)[/tex]

Therefore, the equation of a straight line is:

[tex]y-y_{0}=m(x-x_{0})[/tex]

[tex]y-y_{0}=m(x-x_{0}) \\ \\ y-20=\frac{70-20}{140-0}(x-0) \\ \\ \boxed{y=\frac{5}{14}x+20}[/tex]

b. Graph.

For Plan B we know that it offers a fixed payment of $30 plus 25¢ per mile. We know that 1¢ is equivalent to $0,01, therefore 25¢ = $0,25. Therefore, we can write the plan as a fixed payment of $30 plus $0,25 per mile. This can be written using the following equation:

[tex]\boxed{y=0,25x+30}[/tex]

So the graph is shown below.

c. Explanation.

The line in red represents [tex]y=\frac{5}{14}x+20}[/tex] while the line in blue represents [tex]y=0,25x+30[/tex]. Both Plans offer a fixed payment plus an extra fee per mile. If Trey runs less than 93,333 miles, he needs to rent Plan A because the cost here is less than Plan B. On the other hand, if he runs more than 93,333 miles, he needs to choose Plan B rather than Plan A because the cost of Plan B is less than the cost of Plan A here.

d. Same total cost.

The same total cost occurs when both line intersect, that is, at the point [tex](93.333, 53.333)[/tex]. Hence if Trey runs exactly 93,333 miles, he'll need to pay 53,333$. Therefore, in this situation no matter what plan he chooses because he will pay the same amount of money.