Answer:
See below.
Step-by-step explanation:
A.
The equation of a line is (in slope-intercept form)
y = mx + b
We need to find the slope, m, and the y-intercept for this situation.
Finding the slope:
You already wrote correctly that the difference between each two consecutive values of C(n) is 150. The difference between consecutive values of n is 1. The values we see for n are 2, 3, 4, 5.
n is the number of nights. As the number of nights go up by 1, the cost goes up by $150.
slope = rise/run
For a change of 1 in x (n here, the run), you get a change of 150 in y (C(n) here, the rise)
slope = 150/1 = 150
The slope of the equation is 150.
Now we need to find the y-intercept.
Look at the table.
Here are the first two lines of values.
n C(n)
2 950
3 1100
Since you know that a difference of 1 night creates a difference of $150 in the cost, work backwards, and subtract 1 night and 150 from the top line. You get this new top line (in bold):
n C(n)
1 800
2 950
3 1100
Subtract again 1 night and 150 from the cost, and you get this (new line in bold):
n C(n)
0 650
1 800
2 950
3 1100
For 0 nights, the cost is $650. The y-value at x = 0 is the y-intercept. That means the y-intercept is 650. b = 650
Now that we know the slope and the y-intercept, we can write the equation.
y = mx + b
y = 150x + 650
Since you are using n for x and C(n) for y, your equation is
C(n) = 150n + 650
B.
The slope is the cost per night.
C.
The coordinates of the y-intercept are (0, 650).
It represents the initial fee of $650.
D.
We need to find C(10).
In the function C(n), n represents the number of nights.
Since we have C(10), the 10 is replacing n and represents a stay of 10 days.
To find C(10), we use the function.
C(n) = 150n + 650
C(10) = 150(10) + 650
C(10) = 1500 + 650
C(10) = 2150
Meaning: A 10-day stay costs $2150.
E.
C(n) = 1850
The cost of n nights is $1850.
The question is what is the number of nights that costs $1850?
We use the function set equal to 1850 and solve for n, the number of nights.
C(n) = 150n + 650 = 1850
150n + 650 = 1850
Subtract 650 from both sides.
150n = 1200
Divide both sides by 150.
n = 1200/150
n = 8
Answer: $1850 is the cost of an 8-day stay.
