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.
A point (6, comma, 426,42) is labeled below. Which statement about the graph is true?
0
Boxed Lunches Ordered
Total Cost (in dollars)
x
y
0
Boxed Lunches Ordered
Total Cost (in dollars)
(6 , 42)
The unit rate is 7 lunches per dollar
The unit rate is 6 lunches per dollar
The unit rate is $7.00 per lunch
The unit rate is $42.00 per lunch
The statement "The unit rate is 7 lunches per dollar" is true.
To find the unit rate, we can divide the change in y (total cost) by the change in x (boxed lunches ordered) between two points on the graph. Since the point (6, 426.42) is labeled, we can use it along with the point (0, 0) to find the unit rate.
Change in y = 426.42 - 0 = 426.42
Change in x = 6 - 0 = 6
Unit rate = Change in y / Change in x = 426.42 / 6 = 71.07
The unit rate is 7 lunches per dollar.
The statement "The unit rate is $7.00 per lunch" is true.
To find the unit rate on the graph, we can look at the slope of the line connecting two points. In this case, we can calculate the slope using the point (0,0) and (6,426.42):
Slope (m) = (change in y) / (change in x)
= (426.42 - 0) / (6 - 0)
= 426.42 / 6
= 71.07
The unit rate represents the cost per lunch. Since the slope is the cost per lunch, the unit rate is $7.00 per lunch.
To determine the unit rate, we need to find the rate at which the total cost changes with respect to the number of boxed lunches ordered. In other words, we need to find the slope of the graph at the given point (6, 426.42).
To find the slope, we can use the formula:
slope = (change in y)/(change in x)
In this case, the change in y is given as 426.42 (the total cost at x=6), and the change in x is given as 6 (the number of boxed lunches ordered at x=6).
Therefore, the slope/unit rate is:
slope = 426.42/6
slope ≈ 71.07
Now, to interpret the unit rate, we consider the y-axis which represents the total cost in dollars and the x-axis which represents the number of boxed lunches ordered.
The given slope of 71.07 represents the change in total cost for every unit increase in the number of boxed lunches ordered. Therefore, the unit rate is 71.07 dollars per boxed lunch.
Hence, the statement "The unit rate is $71.07 per lunch" is true.