20110802: Exploring Equations Visually

Today, we looked at equations in a different form using Grapher.

Part 1:
Algebraically, solving equation x + 8 = 9 will give us x = 1
In Grapher, the same equation looks like this 
 

Observation: 
The answer of the equation is shown by the line that cuts across the x axis in the graph. This line is parallel to the y axis.
We conclude that 
the solution of an equation (with one unknown) can be represented as a vertical line, cutting the x axis at the value found when the equation is solved algebraically.


If we were to change the variable x to y, the equation becomes y/3 - 2 = 0:
The answer would now be represented by a horizontal line cutting across the y axis at 6. This line is also parallel to the x axis.



Part 2:
Given the three equations:
  • 20x – 100 = 0
  • 2(x – 7) = –4 
  • (5x - 11)/7 = 2
When we solve these 3 questions, they all resulted in the same value of x, which is 5.
Graphically, we get
We observe that
The lines generated by the 3 equations overlap each other because all have the same value, 5.
Hence these equations are known as equivalent equations.

Follow-up: Complete the Exploration worksheets and hand-in by the end of the day.

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