A store sells a 1-liter container of juice for 75¢ and a 2-liter container for $1.40. Assume that the cost varies linearly with the number of liters, and find the slope of the line that shows the relationship. How many liters would be in a container that cost $3.35?
The School Subject is not Tim, but MATH.
Sra
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To find the slope of the line that represents the relationship between the cost and the number of liters, we need to use the formula for calculating the slope:
Slope = (change in y) / (change in x)
In this case, the cost in cents represents the y-axis, and the number of liters represents the x-axis.
Let's define the points (x1, y1) and (x2, y2) as follows:
Point 1: (1, 75) - 1-liter container for 75¢
Point 2: (2, 140) - 2-liter container for $1.40
The change in y is calculated as y2 - y1, and the change in x is calculated as x2 - x1.
Change in y = 140 - 75 = 65 cents
Change in x = 2 - 1 = 1 liter
Now, substituting these values into the slope formula:
Slope = (65 cents) / (1 liter)
Slope = 65 cents/liter
So, the slope of the line that represents the relationship between the cost and the number of liters is 65 cents per liter.
Now, to determine the number of liters in a container that costs $3.35, we can use the slope-intercept form of a linear equation:
y = mx + b
Since the cost varies linearly with the number of liters, we can rewrite the equation as:
cost = slope * liters + b
We know the cost ($3.35) and the slope (65 cents/liter), so we can substitute these values into the equation:
3.35 = 65 * liters + b
Now, we need to find the value of b, which represents the y-intercept. To do this, we can use one of the given points (x1, y1) on the line, such as (1, 75).
75 = 65 * 1 + b
75 = 65 + b
b = 75 - 65
b = 10
Now we have the equation:
cost = 65 * liters + 10
To find the number of liters that costs $3.35, we can rearrange the equation and solve for liters:
3.35 = 65 * liters + 10
3.35 - 10 = 65 * liters
-6.65 = 65 * liters
liters = -6.65 / 65
Therefore, the number of liters in a container that costs $3.35 is approximately -0.102 liters. However, it is not possible to have a negative amount of liters in a container, so in this case, it does not make sense to ask for the number of liters.