Question

what does the slope of the line tell you about the situation? there are 50 scoops of popcorn in the container to start. vivian fills each bag with 2 scoops of popcorn. vivian fills each bag with 5 scoops of popcorn.

Explanation:

Step1: Identify two points on the line

We can see from the graph that when \( x = 0 \) (bags filled = 0), \( y = 50 \) (scoops remaining), and when \( x = 20 \) (bags filled = 20), \( y = 10 \) (scoops remaining). So the two points are \((0, 50)\) and \((20, 10)\).

Step2: Calculate the slope

The formula for slope \( m \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the values from the points: \( m=\frac{10 - 50}{20 - 0}=\frac{- 40}{20}=- 2 \). The negative sign indicates a decrease. The slope's magnitude (2) represents the rate of change of scoops remaining with respect to bags filled. Since the slope is -2, it means for each bag filled (increase in \( x \) by 1), the scoops remaining ( \( y \)) decrease by 2. So Vivian fills each bag with 2 scoops of popcorn.

Answer:

Vivian fills each bag with 2 scoops of popcorn.