Part A: Jake rented a kayak at $26 for 3 hours. If he rents the same kayak for 5 hours, he has to pay a total rent of $42. Write an equation in the standard form to represent the total rent (y) that Jake has to pay for renting the kayak for x hours. (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)

Let
a = initial cost to rent a kayak
b = rental rate, $/hour
x = hours for which the kayak is rented
y = total rent

It costs $26 to rent a kayak for 3 hours, therefore
a + 3b = 26 (1)
It costs $42 to rent a kayak for 5 hours. Therefore
a + 5b = 42 (2)

Subtract (1) from (2).
a + 5b - (a + 3b) = 42 - 26
2b = 16
b = $8 per hour
From (1), obtain
a = 26 - 3*8 = $2

Part (a)
The total rent is represented by
y = 2 + 8x

Part (b)
In functional notation form,
f(x) = 2 +8x

Part (c)
To graph this function, create a table as shown below.
x f(x)
--- ------
0 2
1 10
2 18
3 26
4 34
5 42

The graph is shown below. Note that y = f(x).