Questions: Researchers conducted an observational study of automobile drivers and their cell phone use by manually observing traffic in heavily congested areas. They would record the amount of time they observed individual drivers on the phone while operating their vehicle in stop and go traffic and the number of accidents on a particular section of highway over the course of a month. The accompanying graph depicts the data they recorded, each point represents a 1 mile section of heavily congested roads. If the x and y variables were swapped, what would the new slope be?

Researchers conducted an observational study of automobile drivers and their cell phone use by manually observing traffic in heavily congested areas. They would record the amount of time they observed individual drivers on the phone while operating their vehicle in stop and go traffic and the number of accidents on a particular section of highway over the course of a month.

The accompanying graph depicts the data they recorded, each point represents a 1 mile section of heavily congested roads.

If the x and y variables were swapped, what would the new slope be?

Transcript text: Researchers conducted an observational study of automobile drivers and their cell phone use by manually observing traffic in heavily congested areas. They would record the amount of time they observed individual drivers on the phone while operating their vehicle in stop and go traffic and the number of accidents on a particular section of highway over the course of a month. The accompanying graph depicts the data they recorded, each point represents a 1 mile section of heavily congested roads. If the $x$ and $y$ variables were swapped, what would the new slope be?

Solution

Solution Steps

Step 1: Understand the Problem

Researchers conducted an observational study to examine the relationship between the average length of phone calls made by drivers and the number of car accidents in heavily congested areas. The graph provided shows the data collected, with each point representing a 1-mile section of heavily congested roads.

Step 2: Identify the Variables

X-axis (Independent Variable): Average length of phone calls (minutes)
Y-axis (Dependent Variable): Number of car accidents

Step 3: Analyze the Graph

The graph shows a positive correlation between the average length of phone calls and the number of car accidents. As the average length of phone calls increases, the number of car accidents also tends to increase.

Final Answer

If the x and y variables were swapped, the new slope would be the reciprocal of the original slope. This is because the slope of a line is defined as the change in the y-variable divided by the change in the x-variable. Swapping the variables would invert this ratio.

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