Many different quantities exhibit a linear relationship, in which the rate of change of one quantity with respect to another is constant. For example, if a car is traveling at a constant speed of 55 miles per hour on a highway, the relationship between the time spent on the road and the distance traveled is linear; during each hour, the car travels 55 miles, so that as time goes on the distance travels increases at a constant rate.
In this unit you will learn how linear relationships between quantities can be represented by equations containing two variables, as well as by graphs on the coordinate plane. Several different methods of graphing equations will be discussed, and special cases such as horizontal lines and vertical lines will be considered. The connection between the slope, or steepness, of a line and its equation will also be explored.
Guiding Questions for Unit 2:
How do graphs help to visualize numerical concepts?
How does our understanding of geometry (space) enhance our understanding of algebra (numbers)?
How are rates of change and slopes related?
What are the relationships between the various forms of a linear equation and its graph?
Lessons in Unit 2:
Lesson 1: The Coordinate Plane
Lesson 2: Graphing Linear Equations Using a Table
Lesson 3: Horizontal Lines and Vertical Lines
Lesson 6: Slope-Intercept Form