Question

every halloween, trick-or-treaters love going to janelles house to see her spooky decorations and get some of her delicious caramel chews. there is a proportional relationship between the number of kids in a group, x, and the total number of caramel chews janelle gives to that group, y.

Explanation:

Since the problem involves a proportional relationship (a linear relationship through the origin) between the number of kids (\(x\)) and the number of caramel chews (\(y\)), we can find the constant of proportionality (slope) using the formula for a proportional relationship \(y = kx\), where \(k=\frac{y}{x}\).

Step 1: Identify a point on the line

From the graph, we can see that when \(x = 1\) (assuming the grid lines are at integer values, and looking at the slope), let's check a clear point. For example, when \(x = 2\), \(y = 6\)? Wait, no, let's take a better point. Wait, the line passes through, for example, when \(x = 1\), \(y = 3\)? Wait, no, let's check the slope. Wait, if we take two points: let's say when \(x = 2\), \(y = 6\) (since from the graph, the line goes up 6 when \(x\) increases by 2? Wait, no, let's look at the grid. The y - axis is caramel chews, x - axis is number of kids. Let's take a point where \(x = 2\), \(y = 6\) (since the line passes through (2,6)? Wait, no, maybe (1,3)? Wait, let's calculate the slope. Let's take two points. Let's say when \(x = 2\), \(y = 6\) (because from the origin, if we move 2 units in x, we move 6 units in y). Then the slope \(k=\frac{y}{x}=\frac{6}{2} = 3\). Wait, or when \(x = 3\), \(y = 9\), \(k=\frac{9}{3}=3\). So the equation is \(y = 3x\).

But since the problem is not fully stated (like finding the equation, or finding \(y\) for a given \(x\), or \(x\) for a given \(y\)), but assuming we need to find the constant of proportionality (the number of caramel chews per kid).

Step 2: Calculate the constant of proportionality

Using the formula \(k=\frac{y}{x}\). Let's take a point from the graph. Let's say when \(x = 2\), \(y = 6\) (from the graph, the line passes through (2,6)). Then \(k=\frac{6}{2}=3\). So the constant of proportionality is 3, meaning Janelle gives 3 caramel chews per kid.

If the question was to find the number of caramel chews per kid (the constant of proportionality), the answer is 3.

Answer:

The constant of proportionality (number of caramel chews per kid) is \(\boldsymbol{3}\). (If the question was different, adjust accordingly, but based on the proportional relationship, the slope \(k = 3\))