Part a: amir rented a scooter at $43 for 3 hours. if he rents the same scooter for 8 hours, he has to pay a total rent of $113. write an equation in the standard form to represent the total rent (y) that amir has to pay for renting the scooter 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)

Part A: Amir rented a scooter at $43 for 3 hours. If he rents the same scooter for 8 hours, he has to pay a total rent of $113. Write an equation in the standard form to represent the total rent (y) that Amir has to pay for renting the scooter for x hours. (4 points)

time          rent
hours          $

3                 43
8               113

Assume a linear relation, this is r(t)= Ax + C

=> [r - 43] / [ x - 3] = [113 - 43] / 8 - 3]

=> [r - 43] / [x - 3] = 70 / 5

=> [r - 43] / [x - 3] = 14

=> r - 43 = 14 [x - 3]

=> r - 43 = 14x - 14*3

=> r - 43 = 14x - 42

=> r - 14x - 1 = 0   < standard form

Part B: Write the equation obtained in Part A using function notation. (2 points)

r - 14x - 1 = 0  => r(x) = 14x + 1  < function notation, r(x)

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)

1) Horizontal axis = x

2) Vertical axis = y

3) Domain x > 0 = [0, ∞)

4) Range r > 0 = [0, ∞)

5) r-intercept=> x = 0 => r = 14(0) + 1 = 1 => (0,1)

6) slope: 14

7) x-intercept => r = 0 => 0 = 14x + 1 => x = -1/14 => (-1/14, 0)