Graph Proportional Relationships Quick Check
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Question
Use the image to answer the question.
A line graph titled 5 Kilometer Run shows time in minutes on the x-axis and distance in kilometers on the y-axis. The graph shows the trend for four participants: Bella, Ruby, Greg, and Paul. The x-axis ranges from 0 to 60 in increments of 10. The y-axis ranges from 0 to 15 in increments of 2.5. A line labeled Bella starts at the origin and passes through plotted point left parenthesis 45 comma 3.5 right parenthesis. A line labeled Ruby starts at the origin and passes through plotted point left parenthesis 40 comma 2.5 right parenthesis. A line labeled Greg starts at the origin and passes through plotted point left parenthesis 45 comma 2.5 right parenthesis. A line labeled Paul starts at the origin and passes through plotted point left parenthesis 25 comma 1 right parenthesis.
Four friends ran a 5K to raise money for their school. The graph shows their rates as a ratio of distance measured in kilometers and time in minutes. Based on the points shown, name the person who ran 212 km in 45 minutes.
(1 point)
Responses
Paul
Paul
Ruby
Ruby
Greg
Greg
Bella
Bella
Paul
Based on the information provided in the graph, the person who ran 212 km in 45 minutes is Bella.
To answer this question, we need to identify the line that represents the rate for running 212 km in 45 minutes. Let's analyze the given information to find the correct line:
- The line labeled Bella passes through the point (45, 3.5).
- The line labeled Ruby passes through the point (40, 2.5).
- The line labeled Greg passes through the point (45, 2.5).
- The line labeled Paul passes through the point (25, 1).
Based on the points shown, we want to find the line that represents running 212 km in 45 minutes.
To determine this, we need to find which line has a slope that corresponds to the rate of 212 km in 45 minutes. The slope represents the ratio of the change in distance to the change in time.
First, we calculate the slope for each line using the formula:
Slope = (change in y) / (change in x)
Let's calculate the slopes for each line:
- For Bella's line, the change in y = 3.5 - 0 = 3.5 and the change in x = 45 - 0 = 45. Therefore, the slope for Bella's line is 3.5/45 = 0.078.
- For Ruby's line, the change in y = 2.5 - 0 = 2.5 and the change in x = 40 - 0 = 40. Therefore, the slope for Ruby's line is 2.5/40 = 0.063.
- For Greg's line, the change in y = 2.5 - 0 = 2.5 and the change in x = 45 - 0 = 45. Therefore, the slope for Greg's line is 2.5/45 = 0.056.
- For Paul's line, the change in y = 1 - 0 = 1 and the change in x = 25 - 0 = 25. Therefore, the slope for Paul's line is 1/25 = 0.04.
Now we compare the slopes to find the line that represents running 212 km in 45 minutes. The closest match is the line with the slope of 0.078, which corresponds to Bella's line. Therefore, the person who ran 212 km in 45 minutes is Bella.
So the correct answer is: Bella.