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?

I know that I need to assume the Cost is y (in cents) and the number of liters is x.
75 = m + b
140 = 2m + b
but I don't know how to find how many liters would be in a container that cost $3.35?

treat your data as two ordered pairs (1,75) and (2,140)

slope = (140-75)/(2-1) = 65/1

So Cost = 65L + b
using (1,75)
75 = 65(1) + b
b = 10

cost equation:
C = 65L + 10

(I guess you can buy an empty carton for 10 cents, lol)

so if C = 335
335 = 65L + 10
65L = 325
L = 5

To find the slope of the line that shows the relationship between the cost and the number of liters, we can use the given information.

Let's assume the cost is denoted by "y" and the number of liters is denoted by "x". From the given information, we have two data points:

Point 1: (1 liter, 75 cents) - (x1, y1)
Point 2: (2 liters, $1.40) - (x2, y2)

Using the slope formula, we can calculate the slope (m) of the line as follows:

m = (y2 - y1) / (x2 - x1)

Plugging in the values:

m = (1.40 - 0.75) / (2 - 1) = 0.65 / 1 = 0.65

Therefore, the slope of the line that shows the relationship between cost and the number of liters is 0.65.

Now, to find the number of liters in a container that costs $3.35, we will use the slope-intercept form of a linear equation, which is:

y = mx + b

Here, "y" represents the cost, "m" represents the slope, "x" represents the number of liters, and "b" represents the y-intercept.

We can rearrange the equation as:

x = (y - b) / m

Since we know the slope (m) is 0.65, we need to determine the y-intercept (b).

Using the first data point (1 liter, 75 cents), we can substitute these values into the equation to solve for b:

75 = 0.65(1) + b

Simplifying, we have:

75 = 0.65 + b
b = 75 - 0.65
b ≈ 74.35

Now we have the values we need to find the number of liters in a container that costs $3.35. Substituting the values into the equation:

x = (3.35 - 74.35) / 0.65
x = -71 / 0.65
x ≈ -109.23

Since the number of liters cannot be negative, we can conclude that a container that costs $3.35 would contain approximately 109.23 liters (rounded to the nearest whole number).