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)