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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, but taken we are in Denmark and are part of a Danish school the equation would be:  Where:    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.

•    Middle

1. Given two points, (2,4) and (1,2), find the equation of the following straight line.   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:   Where:  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:  Then, in this case ‘a’ and ‘c’ are the slopes of the two lines.

Conclusion

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Appendix

Slope Formula:        Notation

Different Countries teach different "notation".

US, Canada, Egypt, Mexico, and Philippines: 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: Albania, Brazil, Czech Republic, Denmark, Ethiopia, France, Lebanon, Holland, Kyrgyzstan and Vietnam: Azerbaijan, China, Finland, Russia and Ukraine: Greece: Italy: Japan: Latvia: Romania: Sweden: Slovenia: 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.

 See ’Notation’ in the Appendix

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