Lesson 2

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1. Lesson 2

Mathematics 30-3 Module 3

Module 3: Algebra


Lesson 2: Equation of a Line



Have you ever tried to bike up a steep hill? The steepness of an incline is measured using a grade. A grade is the ratio of the rise of an incline to its run. If a hill rises 100 m for every 1000 m of run, you would say the hill’s grade is  or 0.1. Most road signs show the grade as a percent. Recall from Mathematics 20-3 that




Therefore, if the rise is 100 m and the run is 1000 m, the grade would be 10%, calculated as follows:




These are photographs of Baldwin Street in Dunedin, New Zealand.

Left: Ullisan/flickr; top right: RabunWarma/flickr; bottom right: Ullisan/flickr.

All images used under Creative Commons Licence (2.0 Generic). Attribution-NoDerivs).

Have you ever noticed that the middle of the road is slightly higher than at the road’s curbs? This is because roads are built with at least a 1% grade so that water will run off to the sides of the road. When building wheelchair ramps the grade is not to exceed 1:12, or about 8.3%.


Baldwin Street in Dunedin, New Zealand, is the world’s steepest street, according to the Guinness Book of Records. The grade of Baldwin Street is approximately 35%. Do you think you could peddle up Baldwin Street?


Lesson Outcomes


At the end of this lesson you will be able to

  • determine the slope from a pair of points, and then come up with the equation of a line
  • create a table of values and be able to write a linear equation in the form
Lesson Questions

You will investigate the following questions:

  • How does the equation of a linear function relate to the function’s graph?
  • How are the properties of linear functions applied to studying and solving problems?


Your assessment may be based on a combination of the following tasks:

  • completion of the Lesson 2 Assignment (Download the Lesson 2 Assignment and save it in your course folder now.)
  • course folder submissions from Try This and Share activities
  • additions to Glossary Terms and Formula Sheet
Materials and Equipment


You will need