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?

show your work here

\\( \circ\\ y = -1.4x + 13 \\) \\( \circ\\ y = -14x + 13 \\)
\\( \circ\\ y = 1.4x + 1 \\) \\( \circ\\ y = -7x \\)

Explanation:

Step1: Analyze the trend direction

The scatter plot shows that as \( x \) (minutes after the bell) increases, \( y \) (number of students left) decreases. So the slope of the trend line should be negative. This eliminates the option \( y = 1.4x + 1 \) (positive slope).

Step2: Analyze the magnitude of the slope

Let's check the rate of change. At \( x = 0 \), the \( y \)-intercept is around 12 - 13 (from the first point). Let's take two points, say \( (0, 12) \) and \( (8, 3) \). The slope \( m=\frac{3 - 12}{8 - 0}=\frac{-9}{8}=- 1.125\), which is close to - 1.4. The slope of \( y=-14x + 13\) is - 14, which is too steep (a slope of - 14 would mean at \( x = 1 \), \( y=-14 + 13=-1\), which is not reasonable as the number of students can't be negative so early). The slope of \( y = - 7x\) is - 7, which is also too steep (at \( x = 1 \), \( y=-7\), not reasonable). So the only reasonable slope with a negative value and reasonable magnitude is - 1.4, and the \( y \)-intercept around 13. So the equation \( y=-1.4x + 13\) fits.

Answer:

\( y = - 1.4x + 13 \)