Intro+to+Linear+Relations

= Introduction to Linear Relations, Graphing and Slopes =

A linear relation exists between two variables if, when their values are plotted on a graph, it ends up with a straight line or values that can average to be a straight line. There is no value in a linear relation which has a power greater than one and each of the variables are directly related to each other (i.e. if one variable changes, the other also changes by the same value).

Linear Relations follow the following formula:

 * //y = mx + b//**

Where:
 * //x//** is the value of the coordinate on the x - axis
 * //y//** is the value of the coordinate on the y - axis
 * //m//** is the value of the slope of the line (y versus x)
 * //b//** is the y - intercept (the point where the line touches the y axis)

The value of any unknown variable can be solved for algebraically.

Linear Relations are Plotted on the Following Graph:


Note: For any graph, the following requirements **//must always//** be met.
 * ~ ✓ ||~ graphing ||
 * ☐ || axes labeled ||
 * ☐ || axes to infinity, as appropriate ||
 * ☐ || origin labeled ||
 * ☐ || ticks across axes ||
 * ☐ || each axis evenly and widely spaced ||
 * ☐ || points labeled with coordinate pair and optional label ||
 * ☐ || graph titled ||

**Calculating Slopes:**
A slope is calculated by the following formula:


 * //slope = rise/run//**

The //**rise**// of a line is the height of the line (from the origin) on the y axis (its y coordinate). The **//run//** of a line is the length of the line (from the origin) on the x axis (its x coordinate).

The slope of a line makes it easy to determine if the line is ascending or descending. If the slope has a positive value, the line is ascending but if the line has a negative value, it is descending.



**How to Read the Point of Intersection in a Linear Relation:**
The point of intersection in a linear relation is the point where two line meet or intersect. Like any other point in a graph, this point has its own coordinates which distinguish it and tell us where to 'find' it.