Question

brycen plots this graph of y, the number of students left in the classroom x minutes after the bell has rung. which of the following equations describes a reasonable trend line for the data shown in the scatter plot? (scatter plot image omitted) show your work here

Explanation:

Step1: Identify Trend Direction

The scatter plot shows a negative correlation (as \( x \) increases, \( y \) decreases), so the slope \( m \) of the trend line should be negative.

Step2: Estimate Intercept and Slope

• At \( x = 0 \) (when the bell rings), the number of students \( y \) is around 12 (intercept \( b \approx 12 \)).
• Pick two points: (0, 12) and (8, 3). The slope \( m=\frac{3 - 12}{8 - 0}=\frac{-9}{8}\approx - 1.125 \), close to \( -x \) or \( -1.1x \). A reasonable trend line could be \( y=-x + 12 \) (or similar with negative slope and intercept ~12).

Answer:

A reasonable trend line is \( \boldsymbol{y=-x + 12} \) (or equivalent negative - slope line with intercept ~12, e.g., \( y=-1.1x + 12 \)).