Part A: Abe rented a bike at $36 for 5 days. If he rents the same bike for 8 days, he has to pay a total rent of $48. Write an equation in the standard form to represent the total rent (y) that Abe has to pay for renting the bike 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) (10 points)

Equation of the system is y = 4x + 16 and in function form is f(x) = 4x + 16.

Step-by-step explanation:

A. We are given that, the rent for 5 days is $36 and for 8 days is $48 i.e. in the tuple form we get the points (x,y) = (5,36) and (8,48) where x= no. of days for which the bike is rented and y= rent in dollars.

Now, using these two points we will find the slope ‘m’ of the function.

i.e. m = frac{48-36}{8-5}

i.e. m = 4.

Now, the general form of the straight line is y = mx + b, where b is the y-intercept.

Using the point (x,y) = (5,36) and slope m = 4, we will find the value of ‘b’ by substitution.

i.e. 36 = 4*5 + b  i.e  b = 16

Hence, the equation of the system is y = 4x + 16.

B. We have to write y = 4x + 16 into function notation i.e. f(x) = y

Hence, function notation is f(x) = 4x + 16.

C. Let x-axis be the number of days for which bike is rented and y-axis be the rent in dollars. Let the intervals be 1 unit apart.

Now, we can find the end points (0,16) and (-4,0). Plot these points and join them, this will give you the graph of the equation as shown below.

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step-by-step explanation:

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