Question

review 1 - item 4420
what does this graph tell you about the price of almonds?
the quotient 2.3/0.45 is the price per pound of almonds.
the unit price is zero at the origin.
almonds cost 45 cents per pound.
2.3 pounds cost 45 cents.
(graph: price of almonds with x-axis weight (lb), y-axis price ($), point (0.45, 2.3))

Explanation:

Step1: Understand the concept of unit - price

The unit - price (price per pound) of a product in a price - weight relationship is calculated by the formula \(k=\frac{y}{x}\), where \(y\) is the price and \(x\) is the weight.

Step2: Analyze the given point \((0.45,2.3)\)

In the coordinate \((x,y)=(0.45,2.3)\), \(x = 0.45\) represents the weight (in pounds) and \(y = 2.3\) represents the price (in dollars). The formula for the price per pound (unit - price) is \(k=\frac{y}{x}\). Substituting \(x = 0.45\) and \(y = 2.3\) into the formula, we get \(k=\frac{2.3}{0.45}\).

Step3: Analyze other options

• For the option “Almonds cost 45 cents per pound”: If \(x = 1\) (pound), from \(k=\frac{y}{x}=\frac{2.3}{0.45}\approx5.11\) (dollars per pound), not 0.45 dollars per pound.
• For the option “The unit price is zero at the origin”: The unit price \(k=\frac{y}{x}\), when \(x = 0\) and \(y = 0\), the concept of unit - price (a non - zero division) is not defined in the context of a non - degenerate relationship (a non - vertical line passing through the origin for a proportional relationship).
• For the option “2.3 pounds cost 45 cents”: From the point \((0.45,2.3)\), 0.45 pounds cost 2.3 dollars, not 2.3 pounds cost 0.45 dollars.

Answer:

The quotient \(2.3/0.45\) is the price per pound of almonds.