Question

1. a school collected data on students grade point average, gpa, and average number of hours per day they were on their cell phone and recorded it in the table below.

average # of hours on cell phone / day	1	2	2.5	3	3.5	4	4.5	6	6	6.5	7	7.5	8	8.5

create a scatterplot of this data. what type of function would best represent the relationship?

linear or quadratic

Explanation:

Step1: Identify Variables

Let \( x \) = Average Hours on Cell Phone/Day, \( y \) = GPA. List data points: \((1, 3.8), (2, 3.6), (2.5, 3.7), (3, 3.4), (3.5, 3.2), (4, 3.2), (4.5, 3.1), (6, 2.6), (6, 2.7), (6.5, 2.6), (7, 2.4), (7.5, 2.2), (8, 2.1), (8.5, 2.0)\).

Step2: Analyze Trend

Plotting these (mentally or on paper), as \( x \) increases, \( y \) generally decreases. Check linearity: Calculate slopes between points. From \( x=1 \) to \( x=8.5 \), the slope trend is consistent (negative, roughly constant). Quadratic would have a curve (change in slope direction), but here slope is mostly negative and linear.

Step3: Compare Linear vs Quadratic

Linear functions have constant (or nearly constant) slope. Quadratic has a vertex (slope changes sign). Here, GPA decreases as hours increase, with no upward turn (no vertex), so linear is better.

Answer:

Linear