Question

this graph shows the number of laps that jan runs as her coach times her. what is the slope of the line and what does it mean in this situation? select from the drop - down menus to correctly complete each statement. the slope of the line is choose... this means that jan runs choose... laps every choose...

Explanation:

Step1: Calculate the slope

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(2,4)\) and \((x_2,y_2)=(5,10)\). Then \(m = \frac{10 - 4}{5 - 2}=\frac{6}{3}=2\).

Step2: Interpret the slope

In the context of the graph (where \(x\) - axis is time in minutes and \(y\) - axis is laps run), the slope represents the rate of change of laps with respect to time. A slope of \(2\) means that for every \(1\) unit increase in \(x\) (i.e., every \(1\) minute), \(y\) (the number of laps) increases by \(2\). So Jan runs \(2\) laps every \(1\) minute.

Answer:

The slope of the line is \(2\). This means that Jan runs \(2\) laps every \(1\) minute.