The Straight Line

  A straight line is the shortest distance between
two points.

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The Gradient of a line is a measure of its slope relative to the x axis.

A positive gradient goes upwards, from left to right.

 

2

 

A negative gradient goes downwards, from left to right.

 

3

 

7 6

5 4

Gradient

The gradient is found by dividing the vertical distance by
the horizontal distance.

1

2

gradtri

Examples

 8 3

 

9 4

 

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12

 

find1 eqf1

find2 eqf2

 

Drawing A line from its equation

To draw a line from its equation

 

Example

 

ani1

This gives the points

(0,0) , (1,2) , (2,4), (3,6) and (4,8)

Plotting these points and joining with a straight lines gives

14

Extrapolating the table backwards

15

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       The line y = x has values

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and graph

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Harder lines

Example

ani2

 

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The equation of a straight line

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           y = mx + c
Where m= gradient and c = y-intercept,
the value of y when x is zero.

Example

20

 

Plotting the  graph of  a line from its equation.

Finding the equation of  a line from its graph.

Putting all together.

 

 

© Alexander Forrest