Part A: Maria rented a coat at $285 for 3 days. If she rents the same coat for 6 days, she has to pay a total rent of $510.

Write an equation in the standard form to represent the total rent (y) that Maria has to pay for renting the coat 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.

Joe Mama

This cannot be determined, unless one assumes a model. Assuming a linear model, some fixed base cost, then a per day cost.

Costtotal=costperday*days + fixed
and you have two equations.
285=3x+f
510=6x+f

solving (double the first equation, then subtract it from the second
570=6x+2f
510=6x+f

60=fixed cost
and you solve for the per day cost, x.

Part A: Let's first find the rate at which Maria is charged per day of renting the coat.

From the given information, we can see that the increase in rent from 3 days to 6 days is $510 - $285 = $225. So, the rent increased by $225 in 6 - 3 = 3 days.

Therefore, the rate of increase per day is $225/3 = $75.

Now, let's write the equation in standard form. The initial rent for 3 days is $285. Each additional day increases the rent by $75.

So, the equation in standard form is:
y = 285 + 75x, Where y is the total rent and x is the number of days.

Part B: To write the equation obtained in Part A using function notation, we can use f(x) to represent the total rent.

So, the equation using function notation is:
f(x) = 285 + 75x

Part C: To graph the equation obtained above on the coordinate axes, follow these steps:

1. Label the x-axis as "Number of days" and the y-axis as "Total rent (in dollars)."
2. Choose appropriate intervals for the x-axis and y-axis based on the given information. For example, if Maria rented the coat for a maximum of 10 days, you can choose intervals of 1 for the x-axis from 0 to 10. For the y-axis, choose intervals based on the rent values you get from substituting different values of x into the equation.
3. Plot points on the graph by substituting different values of x into the equation and calculating the corresponding y-values. For example, if x = 0, then y = 285. This gives us one point (0, 285). Similarly, if x = 1, then y = 285 + (75 * 1) = 360. This gives us another point (1, 360). Repeat this process for a few more values of x to get more points.
4. Connect the plotted points with a straight line.
5. Optionally, you can extend the line beyond the given x-axis range to show the trend.

The resulting graph will represent the relationship between the number of days a coat is rented and the total rent charged.

Part A: To write the equation in standard form, we need to determine the rate at which the rent increases per day. We can do this by finding the difference in rent per day:

For 3 days, Maria pays $285. So, for each day, she pays $285/3 = $95.
For 6 days, Maria pays $510. So, for each day, she pays $510/6 = $85.

We can see that the rent decreases by $10 each day. Therefore, the rate of change of the rent per day is -10.

Now, let's express the total rent (y) as a function of the number of days (x) using the slope-intercept form of a linear equation: y = mx + b, where m represents the slope and b represents the y-intercept.

In this case, the slope (m) is -10 (the decrease in rent per day). The y-intercept (b) can be found by substituting the values of x and y from one of the given data points, such as (3, 285).

Using the slope-intercept form, we have y = -10x + b. Substituting the values of (3, 285):

285 = -10(3) + b
285 = -30 + b
b = 285 + 30
b = 315

So, the equation in standard form representing the total rent (y) that Maria has to pay for renting the coat for x days is:

y = -10x + 315

Part B: To write the equation obtained in Part A using function notation, we can express it as:

f(x) = -10x + 315

Part C: To graph the equation f(x) = -10x + 315 on the coordinate axes, follow these steps:

1. Label the x-axis as "Number of Days" and the y-axis as "Total Rent (in dollars)."
2. Choose an appropriate scale for each axis, taking into account the range of values for x and y.
3. Plot the y-intercept, which is the point (0, 315).
4. Determine another point on the graph by selecting a value for x and substituting it into the equation to find the corresponding y-value.
5. Connect the two plotted points with a straight line to represent the equation.
6. Extend the line in both directions to represent all possible x and y values.
7. Add arrows to both ends of the line to indicate that the graph continues indefinitely.

Note: The intervals on the axes would depend on the range of values you choose for x and y. Make sure to adjust the scale on the axes accordingly to represent the entire range of the equation.