- Level: International Baccalaureate
- Subject: Maths
- Word count: 685
The Straight Line
Extracts from this document...
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:
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
Find the y-intercept for the following equation.
Middle
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
Appendix
Proof
Slope Formula:
Slope-Intercept Form:
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.
[1] See ’Notation’ in the Appendix
This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.
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