Graphs of Equations

Examples, solutions, videos, and lessons to help High School students 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).

Suggested Learning Targets

• Understand that all solutions to an equation in two variables are contained on the graph of that equation.

Common Core: HSA-REI.D.10
The graph of an equation in two variables is the set of solutions plotted on a plane (A-REI.10)
How to graph an equation by using a table of values?
How to determine if a coordinate pair is a solution to an equation by using its graph?

Solution Sets to Equations with 2 Variables
Examples:

1. Consider x + 2 = 5. What is the only possible value of x that makes the equation true?
2. Now consider x + y = 5. What are some solutions for x and y that make the equation true?
   Possible solutions can be listed as ordered pairs and graphed.
3. Mrs. Adams has 10 songs on her Spotify playlist. The playlist features songs from her two favorite artists, Shawn Mendes and David Burd (lil Dicky).
   a) Create an equation using two variables to represent this situation.
   b) List at least 3 solutions to the equation you created.
   c) Do you have infinitely many solutions?
   d) Create a graph to represent the solution set.
4. The sum of two numbers is 15.
   a) Create an equation using two variables to represent this situation.
   b) List at least 3 solutions to the equation you created.
   c) How many possible solutions are there to this situation?
   d) Create a graph to represent all the possible solutions.
5. The sum of two integers is 15.
   a) Create an equation using two variables to represent this situation.
   b) List at least 3 solutions to the equation you created.
   c) How many possible solutions are there to this situation?
   d) Create a graph to represent all the possible solutions.

• Show Step-by-step Solutions

Two-variable linear equations and their graphs

• Show Step-by-step Solutions

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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