The Graph of a Linear Equation in Two Variables

Video solutions to help Grade 8 students learn how to predict the shape of a graph of a linear equation by finding and plotting solutions on a coordinate plane.

New York State Common Core Math Grade 8, Module 4, Lesson 13

Worksheets for Grade 8

Lesson 13 Outcome

• Students predict the shape of a graph of a linear equation by finding and plotting solutions on a coordinate plane.
• Students informally explain why the graph of a linear equation is not curved in terms of solutions to the given linear equation.

Lesson 13 Summary

• One way to determine if a given point is on the graph of a linear equation is by checking to see if it is a solution to the equation. At this point, all graphs of linear equations appear to be lines.

Discussion

• In the last lesson we saw that the solutions of a linear equation in two variables can be plotted on a coordinate plane as points. The collection of all points (x, y) in the coordinate plane so that each is a solution of ax + by = c is called the graph of ax + by = c
  
• Do you think it is possible to plot all of the solutions of a linear equation on a coordinate plane?
  
• For that reason, we cannot draw the graph of a linear equation. What we can do is plot a few points of an equation and make predictions about what the graph should look like.
  
• Let’s find five solutions to the linear equation x + y = 6 and plot the points on a coordinate plane. Name a solution.

Exercises 1–6

1. Find at least 10 solutions to the linear equation 3x + y = -8 and plot the points on a coordinate plane. What shape is the graph of the linear equation taking?
2. Find at least 10 solutions to the linear equation x - 5y = 11 and plot the points on a coordinate plane. What shape is the graph of the linear equation taking?
3. Compare the solutions you found in Exercise 1 with a partner. Add their solutions to your graph. Is the prediction you made about the shape of the graph still true? Explain.
4. Compare the solutions you found in Exercise 2 with a partner. Add their solutions to your graph. Is the prediction you made about the shape of the graph still true? Explain.
5. Joey predicts that the graph of -x + 2y = 3 will look like the graph shown below. Do you agree? Explain why or why not.
6. We have looked at some equations that appear to be lines. Can you write an equation that has solutions that do not form a line? Try to come up with one and prove your assertion on the coordinate plane.

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