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GeoGebra

General Form

Author:Ajay Kumar Otta

EQUATION OF A LINE

The general equation of a straight line is of the form where denotes a point in the Cartesian plane which sits on the line and the coefficients a,b,c are constants which determine the orientation of the line.

Drag the sliders and notice the equation. Observe how a,b,c change the straight line.

Point To Think

What makes the equation have a straight graph? How can we be sure? Proof: Let , and be any three points on the line. Then we must have , and. On subtraction we get and . Using these two it follows that . This shows that slopes of AB and BC are equal. Hence the proof.
Let us now answer some simple questions.

Q.1

Which of the coefficients affect the slope of the line?

Select all that apply
  • A
  • B
  • C
  • D
  • E
Check my answer (3)

Q.2

Why does the line vanish when you put a=0 and b=0 in the input boxes?

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Q.3

Can you now rewrite the general form?

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Q.4

Which of the coefficients generates parallel lines?

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Q.5

A is the point where the line meets the x-axis and B is the point where it intersects the y-axis. Which coefficient changes only A?

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Q.6

Set a=0 , b=1 and c=1 in the input boxes . You will get a horizontal line. What is its equation?

Check my answer

Q.7

Set a=1 , b=0 and c=1 in the input boxes. You will get a vertical line.What is its equation?

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Q.8

For what values of a,b,c you will get a horizontal line at distance of 2 units above x-axis?

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Q.9

For what values of a,b,c you will get a vertical line to the left of y-axis at a distance of 2 units?

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Q.10

Adjust the sliders a and b so that the slope of the line shows m=1. Then adjust c so that the line passes through origin. What is the equation you get?

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Something to ponder about!

A straight line is two dimensional. Meaning, we should need only two parameters to describe it . How come we have three in this case namely the coefficients a , b and c?

Q.11

Can we rewrite the equation so that it will have two coefficients in stead of three?

Check my answer

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