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The Straight Line

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Introduction

06/04 2011                                                                William Frisch Møller and Marta Maillet Tapias, MYP 4, NGG ID

The Straight Line

Slope-Intercept Form

The slope intercept form is probably the most frequently used way to express the equation of a line. The equation can be written in many different ways[1], but taken we are in Denmark and are part of a Danish school the equation would be:image19.jpg

image20.png

Where:

image30.png

image38.png

image47.png

image55.png

The slope-intercept form is a type of linear equation. A linear equation is simply an algebraic equation in which each term is either a constant (fixed number) or the product of a constant and (the first power of) a single variable.

Y-intercept

The Y intercept of a straight line is simply where the line crosses the Y axis, thus it requires no calculation to find.

Examples

  1. Find the y-intercept for the following equation.

  • image56.pngimage56.pngimage00.png

image01.png

...read more.

Middle

  1. Given two points, (2,4) and (1,2), find the equation of the following straight line.

image13.pngimage25.jpg

image26.jpg

Vertical Line

A vertical line is a line of which is parallel to the y-axis, which simply means that all points on the line will have the same x-coordinate. A vertical line is a special case as it has no slope. Or put another way, for a vertical line the slope is undefined. The equation of a vertical line will therefore be:

image28.pngimage28.pngimage27.jpg

Where:

image29.png

image31.png

Notice that the equation is independent of y. Any point on the vertical line satisfies the equation.

Perpendicular Lines

Perpendicular lines are straight lines of which intersect to form a 90o angle (right angle). Take two different lines:

image32.png

image33.png

Then, in this case ‘a’ and ‘c’ are the slopes of the two lines.

...read more.

Conclusion

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image18.png

Appendix

Proof

Slope Formula:

image41.jpgimage03.pngimage04.pngimage02.pngimage07.pngimage05.pngimage06.png

image08.png

Slope-Intercept Form:image42.jpg

image09.png

image10.png

Notation

Different Countries teach different "notation".

US, Canada, Egypt, Mexico, and Philippines:        

image43.png

UK, Australia, Bahamas, Bangladesh, Belgium, Brunei, Cyprus, Germany, Ghana, India, Indonesia, Ireland, Jamaica, Kenya, Kuwait, Malaysia, Malawi, Malta, Nepal, Netherlands, New Zealand, Nigeria, Pakistan, Singapore, Solomon Islands, South Africa, Sri Lanka, Turkey, UAE, Zambia and Zimbabwe:

image44.png

Albania, Brazil, Czech Republic, Denmark, Ethiopia, France, Lebanon, Holland, Kyrgyzstan and Vietnam:        

image45.png

Azerbaijan, China, Finland, Russia and Ukraine:        

image46.png

Greece:

image48.png

Italy:        

image49.png

Japan:        

image50.png

Latvia:        

image51.png

Romania:        

image52.png

Sweden:        

image53.png

Slovenia:        

image54.png

The point is that it does not matter whether the ‘slope/gradient’ is defined as an ‘m’, ‘a’ or a ‘b’, as all three letters ultimately represent the same initial thing.


[1] See ’Notation’ in the Appendix

...read more.

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