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Problem-Solving and Data Analysis / Two-variable data: Models and scatterplots Difficulty: Easy

The figure presents the graph of a curve in a coordinate plane, titled “Braking Distance versus Speed.” The horizontal axis is labeled “Speed, in miles per hour,” and the numbers 0 through 80, in increments of 20, are indicated. The vertical axis is labeled “Braking distance, in feet,” and the numbers 0 through 600, in increments of 100, are indicated. Note that all of the following coordinate values are approximate. The graph starts at the origin, and moves steadily upward and to the right, passing through the point with coordinates 20 comma 50, the point with coordinates 40 comma 150, and the point with coordinates 60 comma 300. The graph then goes upward more rapidly as it moves to the right and ends approximately at the point with coordinates 80 comma 600.

The graph above shows the relationship between the speed of a particular car, in miles per hour, and its corresponding braking distance, in feet. Approximately how many feet greater will the car’s braking distance be when the car is traveling at 50 miles per hour than when the car is traveling at 30 miles per hour?

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Explanation

Choice B is correct. According to the graph, when the car is traveling at 50 miles per hour, the braking distance is approximately 225 feet, and when the car is traveling at 30 miles per hour, the braking distance is approximately 100 feet. The difference between these braking distances is $225 minus 100$ , or 125 feet.

Choice A is incorrect and may result from finding the braking distance for 20 miles per hour, the difference between the given speeds. Choice C is incorrect and may result from subtracting the speed from the braking distance at 50 miles per hour. Choice D is incorrect and may result from finding the difference in the braking distances at 60 and 20 miles per hour.