Question

preston buys a large bag of beads to make key chains for a craft festival. he pulls beads from the bag to make each key chain. this situation can be modeled as a linear relationship. complete the statement that describes the situation. preston starts with a bag of blank beads. he uses blank beads to make each key chain.

Explanation:

Step1: Find initial number of beads

The y - intercept of the linear graph represents the initial number of beads (when \(x = 0\), i.e., 0 keychains made). From the graph, when \(x = 0\), \(y=500\). So Preston starts with 500 beads.

Step2: Calculate beads per keychain (slope)

The slope \(m\) of a line is given by \(m=\frac{y_2 - y_1}{x_2 - x_1}\). We can use two points, say \((0,500)\) and \((20,100)\).
\(m=\frac{100 - 500}{20 - 0}=\frac{- 400}{20}=- 20\). The negative sign indicates a decrease, and the magnitude 20 is the number of beads used per keychain.

Answer:

Preston starts with a bag of 500 beads. He uses 20 beads to make each key chain.