Linear Equations
Overview - linear equations
Linear Equations with Two Variables v.s. A Linear Function
Linear Equations with Two Variables are not constrained by a Function's "one-to-one" rule. Or rather, "one-to-one" becomes an unnecessary distraction while we are trying to focus on how two variables freely relate to one another. However, one may argue that a function limiting our view to 'inputs' and 'outputs' with the conventional 'x' and 'y', respectively, helps students build an understanding of variable relationships from a specific case.
You may freely adapt these lessons for functions also.
Some modifications may be necessary, but the main resources for editing are available here.
Grade Level: 9
Overview: After discussion and activity, students will be able to interpret a linear equation and it's graph by connecting the relationship between two variables.
CCGPS 9-12 Standards
Lesson 1: Putting Meaning to Numbers when Setting Up Equations
Linear Equations with Two Variables are not constrained by a Function's "one-to-one" rule. Or rather, "one-to-one" becomes an unnecessary distraction while we are trying to focus on how two variables freely relate to one another. However, one may argue that a function limiting our view to 'inputs' and 'outputs' with the conventional 'x' and 'y', respectively, helps students build an understanding of variable relationships from a specific case.
You may freely adapt these lessons for functions also.
Some modifications may be necessary, but the main resources for editing are available here.
Grade Level: 9
Overview: After discussion and activity, students will be able to interpret a linear equation and it's graph by connecting the relationship between two variables.
CCGPS 9-12 Standards
Lesson 1: Putting Meaning to Numbers when Setting Up Equations
- MCC9-12.A.CED.1 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (underlined portion will be addressed in lesson 2)
- MCC9‐12.F.LE.1b. Recognize situations in which one quantity changes at a constant rate per unit interval
relative to another.
- MCC9-12.A.CED.1 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
- MCC9-12.A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- MGSE9-12.F.LE.5 Interpret the parameters in a linear (f(x) = mx + b) function in terms of context. (In the functions above, “m” and “b” are the parameters of the linear function) In context, students should describe what these parameters mean in terms of change and starting value.