In this lesson, students continue to practice relating the structure of equations to the situation and corresponding graphs. They use their understanding of constraints, equations, and points on a graph to explain whether a graph represents an equation and a situation. Along the way, students practice reasoning quantitatively and abstractly (MP2) and constructing logical arguments (MP3).
Students also work with the structure of linear equations outside of contextual situations. They analyze and rearrange equations to determine the slope and \(y\)-intercept of their graphs and practice explaining their reasoning.
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
- Determine the slope and vertical intercept of the graphs of linear equations by making use of structure or by rearranging the equations.
- Given an equation of the form $ax+by=c$, write an equivalent equation of the form $y=mx+b$.
- Let's analyze different forms of linear equations and how the forms relate to their graphs.
- I can find the slope and vertical intercept of a line with equation $ax+by=c$.
- I can take an equation of the form $ax+by=c$ and rearrange it into the equivalent form $y=mx+b$.
- I can use a variety of strategies to find the slope and vertical intercept of the graph of a linear equation given in different forms.
Equations that have the exact same solutions are equivalent equations.
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