Chapter 5 - Geometry
Page 3 of 7
|Geometry - Euclidean Geometry - Contents|
In geometry certain Euclidean rules for straight lines, right angles and circles have been established for the two-dimensional Cartesian Plane. In other geometric spaces any single point can be represented on a number line, on a plane or on a three-dimensional geometric space by its coordinates. A straight line can be represented in two-dimensions or in three-dimensions with a linear function. A plane can be represented in three-dimensions with an equation such as z = 2x + 3y. Here z is the dependent variable equal to an equation with two independent variables. In Euclidean plane geometry every simple straight line or plane has a unique slope and axis intercept points which can be determined through the equation. For a straight line in two-dimensions the intercept point is where the independent variable equals zero. The slope of a line is defined as the difference between the rise of the y variable over the run of the x variable or just the rise over the run. In viewing the slope as a common fraction the rise is the numerator and the run is the denominator. Any linear equation of the form y = ax + b, where a and b are numeric constants, is a straight line in two-dimensions with a slope equal to the a constant and the intercept point equal to the b constant.
|Geometry - Euclidean Geometry - Examples|
If y = 2x + 1,
the slope of the line is two
and the y intercept point is (0,1).
If y = x/2 - 5,
the slope of the line is one over two
and the y intercept point is (0,-5).
If y = -3x/4 + 1/2, the slope of the line is minus three over four
and the y intercept point is (0,.5).