A company orders boxed lunches from a deli, which all cost the same price. The relationship between the number of boxed lunches ordered, x, and the total cost in dollars of the lunches, y, is represented by the graph below.
What point on the graph represents the unit rate?
0
Boxed Lunches Ordered
Total Cost (in dollars)
x
y
0
Boxed Lunches Ordered
Total Cost (in dollars)
K. left bracket 0 , 0 right bracket(0 , 0)
A. left bracket 9 , 1 right bracket(9 , 1)
C. left bracket 1 , 9 right bracket(1 , 9)
D. left bracket 8 , 72 right bracket(8 , 72)
The point on the graph that represents the unit rate is C. [1, 9] (1, 9).
The point on the graph that represents the unit rate is A. (9, 1).
This is because the unit rate represents the cost per boxed lunch, which is 1 dollar for 1 lunch.
To identify the unit rate on the graph, we need to find the point that represents the cost per boxed lunch.
The unit rate is calculated by dividing the total cost (y) by the number of boxed lunches ordered (x). In other words, it represents the cost per unit of x.
Looking at the given options, we can determine the correct point by considering the ratio of y to x. We want to find the point where this ratio is the same for all points on the line.
Let's calculate the ratios for the options given:
Option K: [0,0]
This point does not provide any information about the cost per unit since there are no boxed lunches ordered. The ratio is undefined in this case.
Option A: [9,1]
The ratio of cost to boxed lunches is 1/9. This means that the deli charges $1 for 9 boxed lunches. However, this does not represent the unit rate.
Option C: [1,9]
Here, the ratio of cost to boxed lunches is 9/1 or simply 9. This tells us that the deli charges $9 for 1 boxed lunch. Again, this does not represent the unit rate.
Option D: [8,72]
The ratio of cost to boxed lunches is 72/8, which simplifies to 9. This means the deli charges $9 for 8 boxed lunches. The ratio of 9 represents the unit rate.
Therefore, the correct answer is option D: [8, 72]. This point on the graph represents the unit rate.