## Lesson 2

### 1. Lesson 2

### Module 3: Algebra

#### Lesson 2: Equation of a Line

##### Focus

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:

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?

###### Assessment

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

- calculator
- straight edge or ruler
- Grid Paper Template