Unit 7: Equations and Graphs of Linear Relations

When travelling on a highway, it is common to estimate driving time by using one hour for every 100 km required. A 200 km trip will take about two hours and a 400 km trip will take about four hours. In this case, the relationship between distance and time is proportional ?" if the distance is doubled, the driving time will also double.

Proportional relationships are one type of relationship that can be represented using linear relations. Although there are many ways of representing relations, two of the most common and most useful are the graph and the equation. This unit will explore these two representations and the relationships between them.

 

Lesson 7.1: Slope-Intercept Form of a Linear Equation

Lesson 7.1 Video link here. (Video under development)

In Unit 1, you used a diagram of a thermometer to convert between the Celsius and Fahrenheit temperature scales. Because the two scales have different zero values, conversion from one scale to the other cannot be accomplished by setting up a simple proportion and solving for an unknown. However, the relationship between Celsius and Fahrenheit is linear and can be represented by a linear equation. Knowing how to manipulate linear equations makes conversions between the two units quite straightforward.

This lesson focuses on the slope-intercept form of linear equations and the graphs of their corresponding relations.