Question

the unruly queens chess club is hosting a tournament, and each club member is bringing something to eat or drink. maddie decides to bring oatmeal raisin cookies from her favorite bakery. this graph shows the relationship between the number of oatmeal raisin cookies maddie buys, x, and their total cost (in dollars), y. do x and y have a proportional relationship? yes no

Explanation:

Step1: Check if the graph is a straight line through the origin

A proportional relationship has a graph that is a straight line passing through the point \((0,0)\). Looking at the given graph, it is a straight - line and passes through the origin \((0,0)\) (since when \(x = 0\) (no cookies bought), \(y=0\) (no cost)).

Step2: Calculate the constant of proportionality (slope)

The formula for the slope \(k\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(k=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points from the graph, say \((2,2)\) and \((4,4)\). Then \(k=\frac{4 - 2}{4 - 2}=\frac{2}{2}=1\). For any other two points (e.g., \((6,6)\) and \((8,8)\)), \(k=\frac{8 - 6}{8 - 6}=\frac{2}{2}=1\). The ratio \(\frac{y}{x}\) is constant for all non - zero values of \(x\) and \(y\) on the line.

Answer:

yes