Linear Equations and their graphs????

Question

I need some explanations and examples????

Answer 1

a linear equation is an equation that forms a straight line on a graph like:
y=mx+b
In this form, the constant m will determine the slope or gradient of the line; and the constant b will determine the point at which the line crosses the y-axis. Equations involving terms such as x2, y1/3, and xy are nonlinear.

http://upload.wikimedia.org/wikipedia/commons/8/80/Linear_functions2.PNG
that is a link to a graph with linear equations

Answer 2

In general a linear equation takes the form y = f(x) where f(x) is a first order function. That is, all x terms have no more than x to the first power (x^1) in them. Such equations are called linear because in their simplest form, they form a straight line.

Linear equations can exist where flat, non-curving surfaces are also defined. Surfaces like these are just higher dimensional versions of a straight line. In some contexts, such surfaces are called branes as in membrane.

An example of a three dimensional linear equation would be z = ax + by + c where z over all x and y points describes a flat surface...a brane. The three dimensions are in the x, y, and z directions in this example. Also note, that when x and y = 0, z = c; so c is the intercept on the z axis. This is very similar to the b intercept term in y = mx + b, which is a common representation of the linear equation for a line.

There is no limit to the number of terms (dimensions) a linear equation can have. But we are unable to graph anything beyond three dimensions (e.g., x, y, z) very well.

Answer 3

A linear equation won't have an exponent greater than one in a variable.
It will be a straight line.
y=2x+1 fits that bill so there's an example for you.
Also, y=6x-5.

Answer 4

y = 2x + 3

2 is the slope, 3 is the point on the y axis.