Part A: Eveline rented a car at $180 for 4 days. If she rents the same car for 9 days, she has to pay a total rent of $325. Write an equation in the standard form to represent the total rent (y) that Eveline has to pay for renting the car for x days. (4 points) Part B: Write the equation obtained in Part A using function notation. (2 points) Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals. (4 points)

Part A. From the problem, we have two sets of data: (1) $180 for 4 days and (2) $325 for 9 days. In formulating relationships as equations, the independent variable is the parameter that we can't control, like time. The dependent variable is the cost of car rental. Thus, we let x be the days and y be the cost. If the equation is linear, its standard form would be: y=mx +b. We use the the two sets of data given to solve for m and b, and complete the equation.

Data point 1 (4,180)
180 = 4m + b
Rearranging, b = 180 - 4m ---> eq 1

Data point 2 (9, 325)
325 = 9m + b ---> eq 2

Substituting eq 1 to eq 2,
325 = 9m + (180-4m)
325-180 = 9m - 4m
5m = 145
m = 29
b = 180 - 4(29) = 64

Therefore, the equation is y = 29x + 64.

Part B. In functional notation, the equation is written as f(x) = 29x + 64.

Part C. To graph the equation, start by making a plot wherein the x-axis is the days while the y-axis is the cost. Then, assign values for x with an interval of 1 unit. See the table shown in the picture. With every value of x, you get a corresponding y value. Then, you plot the points on the cartesian plane. Finally, you connect the data points together forming a straight line.