Graphing Lines

Lines on a graph are an important part of determining the answer in many future equations and problems. No place is better to start than the beginning, lines are hard to describe but are well known as the quickest way to get from one point to another. In the classic euclidean sense, a line is best described as "breadthless length" with a straight line being a line "which lies evenly with the points on itself" so in definition a line has to have points on which it can lie. There are many other definitions that are made and for our purposes of presenting new information it is the best.

    As defined by Descartes, a line is a set of points that forms a linear equation... y=mx+b

• • m is the slope (which I will talk about)

  • b is the y-intercept

  • x is the number entered

  • y is the number that comes out

Slope is the sort of rate at which the line will travel in a sense, as b increases, the steepness of the line is greater. The slope is also known as rise over run in which could be imagined as a right triangle between two points. The line would be the hypotenuse, as in the longest side, while the other parts of the triangle are the x and y axis. The line goes over so many units and then up so many units to get that line. This picture also shows rise over run.

    The rise over run is often needed to be given in terms of x2-x1