Question

heather is working on a science project about sound levels. she asked her classmates to guess the decibel levels of some common sounds. the chart shows the guessed levels and the actual levels of those sounds. using the chart, consider how the graph of the data will appear.

decibel levels of common sounds

event	guessed level	actual level
normal conversation	20	30
restaurant	30	50
normal traffic	65	75
bus interior	45	90
amplified rock music	100	120
jet taking off	130	140+

complete the statements below by dragging the tiles to the slots.

10 negative (10,15) 50 positive (0,0)

the slope of a trend line for these data will be a. the scale for both the horizontal axis and the vertical axis of the graph should be b decibels.

Explanation:

Step1: Analyze the slope

To find the slope, we can use two points. Let's take (0,0) (from Absolute silence) and (30,20)? Wait, no, wait. Wait, the guessed level is the x - value (horizontal axis) and the actual level is the y - value (vertical axis). Let's take two points: (0,0) and (30,20)? No, wait, for normal conversation: guessed = 20, actual = 30. So the points are (guessed, actual). Let's take (0,0) and (20,30). The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{30 - 0}{20 - 0}=\frac{30}{20}=1.5\), or take (20,30) and (30,50): \(m=\frac{50 - 30}{30 - 20}=\frac{20}{10} = 2\)? Wait, maybe a better way. Let's check the difference between actual and guessed. For most points, actual - guessed is positive. For example, normal conversation: 30 - 20 = 10; restaurant: 50 - 30 = 20; normal traffic: 75 - 65 = 10; bus interior: 90 - 45 = 45; amplified rock: 120 - 100 = 20; jet: 140+ - 130 = 10+. So as guessed (x) increases, actual (y) increases, so the slope is positive.

Step2: Analyze the scale

Looking at the data, the decibel levels range from 0 to 140+. The differences between guessed and actual are around 10 - 45, but the scale for the axes (horizontal: guessed, vertical: actual) should be such that we can plot the points. The values are in decibels, and the common differences between the data points (guessed levels: 0,20,30,65,45,100,130; actual levels: 0,30,50,75,90,120,140+). A scale of 10 decibels makes sense because the differences are often multiples of 10 (0,10,20,30,...) or close to it. Also, the point (0,0) is present, and the slope is positive.

For the slope: Since the actual decibel level (y - value) is generally greater than the guessed level (x - value) and as the guessed level increases, the actual level also increases, the slope of the trend line (which measures the rate of change of actual with respect to guessed) will be positive.

For the scale: The decibel values in the data (both guessed and actual) have differences that are often multiples of 10 (e.g., 0, 10, 20, 30, etc.) and a scale of 10 decibels is appropriate to plot the data points (like 0,20,30,65, etc.) clearly.

Answer:

A. positive
B. 10