Linear functions are functions that have x as the input variable, and x has an exponent of only 1. Such functions look like the ones in the graphic to the left. Notice that x has an exponent of 1 in each equation. Functions such as these yield graphs that are straight lines, and, thus, the name linear. Linear functions come in three main forms. An explanation and animation are available for each by clicking the links below. |

Slope-Intercept Form |
A very common way to express a linear function is named the
Or, in a formal function definition:
Basically, this function describes a set, or locus, of (x, y)
points, and these points all lie along a straight line. The
variable holds the
y-coordinate for the spot where the line crosses the y-axis.
This point is called the b.'y-intercept'Click the picture or the link to go on. |

Point-Slope Form |
Technically, one should probably say that the picture to the
left shows the of a line. The statement
does not start with 'y =' or 'f(x)=', so it's not written in a
common equation definition form.
That's not too hard to do, though, with a bit of algebra:function
Or, as a formal function definition:
So where in the equation is the point and the slope of the
line? The variable is a
known point on the line. If you know the slope of and the
coordinates for one point on the line, then you could enter
those values into this equation, and the equation would then
define a set, or locus, of all the points on that line.(x1, y1)Click the picture or the link to go on. |

General Form |
To the left is the ,
A, and B are
three numbers. So the equation could look like this:C
As it turns out, all the points with (x, y) coordinates that would make the above statement true form a line. Using algebra, this general form can be changed into a slope-intercept form, and then you would know the slope and y-intercept for the line. Click the picture or the link to go on. |