Part A: Darla rented a room for 3 days at $285.00 per day. If she rents the same room for 6 days, it would cost $510.
Write an equation in the standard form to represent the total rent (y) that Darla has to pay for renting the room for x amount of 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)
(10 points)
Part A:
To write an equation in standard form to represent the total rent that Darla has to pay for renting the room for x amount of days, we can use the information given in the problem.
Let's denote the total rent as y and the number of days as x.
According to the problem, we know that if Darla rents the room for 3 days, the total cost is $285 per day. This can be expressed as:
Cost for 3 days = $285 * 3 = $855
Similarly, when Darla rents the room for 6 days, the cost is $510. This can be expressed as:
Cost for 6 days = $285 * 6 = $1710
From these two examples, we can see that the cost of renting the room for x days can be calculated using the equation:
y = 285x
This equation represents the total rent (y) that Darla has to pay for renting the room for x number of days.
Part B:
To write the equation obtained in Part A using function notation, we can let the function be represented by f(x). Therefore, the equation becomes:
f(x) = 285x
Part C:
To graph the equation f(x) = 285x on the coordinate axes, follow these steps:
1. Label the x-axis: The x-axis represents the number of days (x). Label it accordingly from 0 to the maximum number of days you want to consider. In this case, we can label it from 0 to 10, as a reasonable range.
2. Label the y-axis: The y-axis represents the total rent (y). Label it accordingly, taking into account the possible range of values. In this case, we know that the total rent can be calculated by multiplying the number of days (x) by 285. Therefore, it would make sense to label the y-axis up to a value higher than the maximum possible total rent. Let's label it up to $2000.
3. Determine the intervals: Choose suitable intervals for both the x-axis and the y-axis. It depends on the range of values you want to display and the scale of the graph you are using. A common choice can be 1 unit for each interval on both axes.
4. Plot the points: Starting from the origin (0, 0), plot the points (x, y) on the graph, where x represents the days and y represents the total rent. Since the equation is a straight line, you only need two points to draw the line.
- Plot the point (3, 855): This represents the cost of renting the room for 3 days.
- Plot the point (6, 1710): This represents the cost of renting the room for 6 days.
You can also plot additional points to verify that the line is straight and consistent with the equation.
5. Draw the straight line: Connect the plotted points with a straight line. Make sure the line extends beyond the plotted points to cover the whole range of possible values.
6. Label the graph: Label the graph with the equation f(x) = 285x to indicate the relationship between x and y.
By following these steps, you will have successfully graphed the equation f(x) = 285x on the coordinate axes.