Part A: Max rented a motorbike at $465 for 5 days. If he rents the same motorbike for a week, he has to pay a total rent of $625.
Write an equation in the standard form to represent the total rent (y) that Max has to pay for renting the motorbike 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)
My answer
Part A
(5,465) (7,625)
slope = 80
y=65+80(x) plug in 5. 65+80(5)
y=65+400.
y=465.
he rents the bike for 5 days he ends up paying $465.
Therefore if he rents it for a week he would be renting it for 7 days (x)days.
y=65+80(7)
65+560.
y=625.
Part B
function notation : f(x) = 80x + 65
Part C
plot two points on the line, and "connect the dots"
x axis is days
y axis is rental in dollars
x-interval is 5 to 7
y-interval is 465 to 625
In Part A, you correctly found the equation to represent the total rent (y) that Max has to pay for renting the motorbike for x days:
y = 80x + 65
In Part B, you also wrote the equation using function notation:
f(x) = 80x + 65
For Part C, to graph the equation on the coordinate axes, follow these steps:
1. Label the x-axis as "Number of days rented" and the y-axis as "Total rent (in dollars)"
2. Choose a suitable scale for both axes, considering the range of values given. For example, you can start the x-axis from 0 and increase by increments of 1, and start the y-axis from 0 and increase by increments of 100.
3. Plot the two points you calculated in Part A: (5, 465) and (7, 625).
4. Connect the two points with a straight line, as the equation represents a linear relationship.
5. Extend the line in both directions to represent all possible values.
To graph the equation y = 80x + 65, you can follow these steps:
1. Label the x-axis as "days" and the y-axis as "rental in dollars."
2. Determine the intervals you want to use for the x-axis. For example, if you want to plot points for x = 0, 1, 2, 3, 4, 5, and so on, you can use increments of 1.
3. Choose a scale for the x-axis and mark the appropriate intervals.
4. Use the equation to calculate the corresponding y-values for each x-value. For example, if x = 0, y = 80(0) + 65 = 65. If x = 1, y = 80(1) + 65 = 145.
5. Plot the points on the graph using the calculated x and y values.
6. Connect the points with a straight line.
In this case, you can start by plotting the two given points: (5, 465) and (7, 625). Mark these points on the graph. Then, using the equation y = 80x + 65, calculate the corresponding y-values for any additional x-values you choose. Plot these points as well, and connect all the points with a straight line.