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Algebraically, lines are relations of input and output that change (increase or decrease) consistently by the simple operations: multiplication, division, addition, and subtraction. An input value produces a predictable output.
Geometrically, lines are straight paths of points that extend endlessly through the plane. They either rise or fall, from left to right, or they go "flat" or "straight up." We generally graph them in a plane on two axes. The horizontal axis represents the input value (we usually call it x) and the vertical axis represents the output value (we usually call it y.)
| the axes are perpendicular |  |
The point where a line crosses an axis is known as an intercept. Since the line is straight it will cross only once, if at all. Horizontal lines may not cross the x-axis (only x = 0 does) and vertical lines may not cross the y-axis (only y = 0) |  |
This line has an x-intercept of (-3,0) and a y-intercept of (0,3) |
Examples of linear equations:
In these equations, the x variable is the input and the y variable is the output.
Since lines behave consistently, one key aspect to link their equation to their graph is their "slope." The slope of a line is its rise or fall from left to right on the coordinate plane.
The slope of a line is the ratio of its "rise" to its "run"
usually expressed as a fraction: 
One form for the equation of line is 
. This is known as the slope-intercept form
because it expresses directly the slope and y-intercept of the line. in the form the variable
"m" stands for the slope and the variable "b"
represents the y-intercept.
In the sample equations given above in slope-intercept form, we can identify the slope and y-intercept
how to have
