The previous lesson looked in depth at an example of a linear relationship that was not proportional and then examined an interpretation of the slope as the rate of change for a linear relationship. In this lesson, slope remains important. In addition, students learn the new term vertical intercept or \(y\)-intercept for the point where the graph of the linear relationship touches the \(y\)-axis.
In the first activity, students match situations to graphs and then interpret different features of the graph (slope and \(y\)-intercept) in terms of the situation being modeled (MP2). In the second activity, students analyze a common error, studying what happens when the slope and \(y\)-intercept are interchanged. This provides an opportunity to see how the \(y\)-intercept and slope influence the shape and location of a line: the \(y\)-intercept indicates where the line meets the \(y\)-axis while the slope determines how steep the line is.
Interpreting features of a graph or an equation in terms of a real-world context is an important component of mathematical modeling (MP4).
- Describe (orally and in writing) how the slope and vertical intercept influence the graph of a line.
- Identify and interpret the positive vertical intercept of the graph of a linear relationship.
Let’s explore some more relationships between two variables.
Print and cut up slips from the Slopes, Vertical Intercepts, and Graphs blackline master. Prepare 1 set of cards for every 2 students.
- I can interpret the vertical intercept of a graph of a real-world situation.
- I can match graphs to the real-world situations they represent by identifying the slope and the vertical intercept.
The vertical intercept is the point where the graph of a line crosses the vertical axis.
The vertical intercept of this line is \((0,\text-6)\) or just -6.
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