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)

We can write the information we know as ordered pairs.  The independent variable, or x, in this case would be the amount of time, and the dependent variable, or y, would be the amount of money.  This is because the amount of money charged changes depending on the amount of time.  This gives us the ordered pairs (3, 26) and (5, 42).  Using the formula for slope we have:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\ \\=\frac{42-26}{5-3} \\ \\=\frac{16}{2}=8[/tex].  A slope of 8 tells us that the hourly rental is $8.  We can use this to back up and see what the rental fee is.  When renting the kayak for 3 hours, Jake paid 26.  We know that it costs $8 per hour; 8(3) = 24.  This leaves us 26-24=$2 for the rental fee.  The equation would then be
y = 8x + 2.
Writing this as a function would be f(x) = 8x + 2.
To graph this, we would label the x-axis as time (hours) and the y-axis as money (dollars).  We would go up to the y-intercept, 2, and plot our point.  (The y-intercept is 2 because in the form y=mx+b, b is the y-intercept; that's where our 2 is.)  From here, we know the slope is 8=8/1, so we would go up 8 and over 1 to the right to plot our next point.  Then we would draw our line between these two points.