Previously, students have written and interpreted equations that model quantitative relationships and constraints. They have also rearranged and solved equations, isolated one of the variables, and explained why the steps taken to rewrite equations are legitimate.
In this lesson, students consider how parts of two-variable linear equations—the parameters and variables—relate to features of the graphs of those equations. They also think about how different forms of two-variable equations affect the information we could gain about the relationships between the quantities and about the graphs. Throughout the lessons, students practice reasoning quantitatively and abstractly (MP2) as they interpret equations and graphs in context.
- Analyze how the numbers in an equation $ax+by=c$ are reflected on its graph and are related to the rate of change in the relationship.
- Graph linear equations of the form $ax+by=c$ and interpret points on the graph in context.
- Understand that different forms of a linear equation can give different insights about the relationship it represents and about the graph.
- Let’s investigate what graphs can tell us about the equations and relationships they represent.
- I can describe the connections between an equation of the form $ax+by=c$, the features of its graph, and the rate of change in the situation.
- I can graph a linear equation of the form $ax+by=c$.
- I understand that rewriting the equation for a line in different forms can make it easier to find certain kinds of information about the relationship and about the graph.
Equations that have the exact same solutions are equivalent equations.
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