The slope of a line can be used to interpret the corresponding linear relation. The following Investigation explores the meaning of slope as more than just the steepness of a line.

Investigation

The following linear relation represents a vehicle's distance travelled over time.

  1. State two points on the graph of the linear relation. Use those points to determine the slope of the relation.


    1. What are the units for the rise of the graph?

    2. What are the units for the run of the graph?


    3. The slope can be determined by dividing the rise by the run. What units are produced if you divide the rise units by the run units? Where have you seen these units before?


    1. Predict the slope of a distance versus time graph representing a vehicle travelling at a constant 40 km/h.


    2. The following table shows data for a car travelling at 40 km/h. Use this data to check your prediction from part a.




  4. Determine the slope of the linear relation represented in the graph.



    1. What are the units of the slope?


    2. What does the slope represent?


  6. The fuel consumption of a vehicle is often measured in units of L/100 km. Determine the fuel consumption represented in the graph in part 4, in units of L/100 km.


  7. The slope of a graph is also referred to as the "rate of change". Explain why.



The slope of a linear relation represents a rate of change. It tells you how much the vertical unit changes for each change of 1 in the horizontal unit.

Rate of Change
how one quantity changes relative to another quantity