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.
Part B: Write the equation obtained in Part A using function notation.
Part C: Describe the steps to graph the equation obtained above on the coordinate axes. Mention the labels on the axes and the intervals
I need help on this one too
Part A: To write an equation in standard form representing the total rent (y) that Max has to pay for renting the motorbike for x days, we can establish a linear relationship between the number of days (x) and the total rent (y).
Let's analyze the given information:
- Max rented the motorbike for 5 days and paid $465.
- If Max rents the motorbike for a week (7 days), he pays a total rent of $625.
To find the equation, we need to determine the rate at which the cost increases per day. From the given information, we can observe that the total rent increases by $160 ($625 - $465) when the number of days increases by 2 (7 - 5).
We can calculate the rate of increase per day by dividing the change in total rent by the change in the number of days:
Rate of increase per day = (Change in total rent) / (Change in number of days)
Rate of increase per day = $160 / 2 = $80
Now, let's determine the initial cost of the motorbike rental if Max were to rent it for 0 days. To do this, we subtract the rate of increase per day multiplied by the number of days from the total rent for the given number of days. In this case, 5 days:
Initial cost of rental = Total rent - (Rate of increase per day * Number of days)
Initial cost of rental = $465 - ($80 * 5) = $465 - $400 = $65
We have established that the initial cost of rental is $65, and the rate of increase per day is $80. Therefore, the equation representing the total rent (y) in terms of the number of days (x) is:
y = mx + b
Where:
m = slope (rate of increase per day) = $80
b = y-intercept (initial cost of rental) = $65
Thus, the equation in standard form is:
y = 80x + 65
Part B: Writing the equation obtained in Part A using function notation, we replace y with f(x) to represent the function:
f(x) = 80x + 65
Part C: To graph the equation f(x) = 80x + 65 on the coordinate axes, follow these steps:
1. Choose a suitable scale for the x-axis and y-axis. Coordinate the scales in proportion to the values you will plot.
2. Label the x-axis as "Number of Days" and the y-axis as "Total Rent."
3. Mark the intervals with the appropriate increments based on your chosen scale. For example, if you choose a scale where each unit on the y-axis represents $10, mark the intervals accordingly.
4. Plot points on the graph by substituting different values of x into the equation f(x) = 80x + 65 and calculating the corresponding y-values.
5. Connect the points linearly using a straight line. Ensure that the line passes through the plotted points.
6. Optionally, add a title to the graph to describe its contents, such as "Total Rent vs. Number of Days."
By following these steps, you will have a graph of the equation f(x) = 80x + 65 on the coordinate axes.
A.625-465=$160
he has to pay for 2 days=160 $
rent paid for 1 day=260/2=$80
amount paid for 5days=8*5=$400
But he paid $465
Difference 465-400=$65
so every one has to pay $65+rent for the no. of days
total rent for x days y=65+80 x (dollars)
B.
f(x)=65+80 x