Question

Part A: Billy rented a canoe at $14 for 2 hours. If he rents the same canoe for 5 hours, he has to pay a total rent of $29. Write an equation in the standard form to represent the total rent (y) that Billy has to pay for renting the canoe 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: Ax By= C

Answer 1

The function in the slope - intercept form:
y = m x + b    It passes through the points ( 2, 14 ) and ( 5, 29 ).
14 = 2 m + b
29 = 5 m + b
-------------------
b = 14 - 2 m
29 = 5 m + 14 - 2 m
29 - 14 - 5 m - 2 m
15 = 3 m
m = 15 : 3
m = 5
b = 14 - 10
b = 4
Part A: y = 5 x + 4
or: 5 x - y = 4  ( in form: Ax + By = C )
Part B :
f ( x ) = 5 x + 4
Part C :
When y = 0
5 x + 4 - 0
5 x = - 4
x = - 4 : 5
x = - 0.8
When x = 0
y = 4.
x - intercept is - 0.8 and y-intercept is y = 4. After that you can graph the function.
For the interval x ∈ ( - ∞, - 0.8 ) the function is negative and for x ∈ ( - 0.8, +∞ ) it is positive.