interpret constant of proportionality in graphs\nclark has a budget of $12 to spend to buy nuts for a party…

interpret constant of proportionality in graphs\nclark has a budget of $12 to spend to buy nuts for a party. the three lines represent the cost of buying bags of three kinds of nuts (walnuts, pecans, or peanuts) of varying weights.\nwhich kind of nut can clark buy the most of with his $12 budget?\nchoose 1 answer:\na walnuts\nb pecans\nc peanuts

interpret constant of proportionality in graphs\nclark has a budget of $12 to spend to buy nuts for a party. the three lines represent the cost of buying bags of three kinds of nuts (walnuts, pecans, or peanuts) of varying weights.\nwhich kind of nut can clark buy the most of with his $12 budget?\nchoose 1 answer:\na walnuts\nb pecans\nc peanuts

Answer

Explanation:

Step1: Recall the relationship between cost, quantity and constant of proportionality

The equation for a proportional relationship is (y = kx), where (y) is the cost, (x) is the quantity (kilograms in this case), and (k) is the constant of proportionality (unit - price). Rearranging for (x), we get (x=\frac{y}{k}). Given (y = 12) (budget), (x) (quantity) is inversely proportional to (k) (unit - price).

Step2: Analyze the slopes of the lines

The slope of a line (y = kx) in the context of cost ((y)) and quantity ((x)) is the unit - price ((k)). A steeper line has a larger slope (higher unit - price). The line for peanuts has the least steep slope, which means it has the lowest unit - price ((k)).

Step3: Use the inverse - proportionality formula

Since (x=\frac{y}{k}) and (y = 12) (constant budget), when (k) (unit - price) is the smallest, (x) (quantity) is the largest. Because peanuts have the smallest (k) (lowest unit - price), for a fixed (y = 12), the value of (x) (kilograms of nuts) will be the largest for peanuts.

Answer:

C. Peanuts