Question

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)

Answer 1

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

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.