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mathematical model
mathematical description of a real-world problem
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Cartesian Coordinate System
System of two perpendicular axes (generally the x- and y-axes) which intersect at the origin. This divides the plane into four quadrants.
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ordered pair
Coordinate pairs like (10,7) and (1,2), where the order is important; the first number in the pair is often called the x-coordinate, whereas the second number in the pair is often called the y-coordinate.
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x-intercept
point at which a graph crosses the x-axis
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y-intercept
point at which a graph crosses the y-axis
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slope of a line
the vertical change (``rise'') divided by the horizontal change (``run'') in a line. Often denoted m. The slope tells us how fast y changes for each unit change in x.
If we know two points on a line, then we can compute the slope m as
(where 
: If two points on a line have the same x-coordinate, we
say that the slope is undefined). This is the ``rise'' (change in y)
over the ``run'' (change in x).
Two lines are parallel if and only if they have the same slope, or if they are both vertical.
Note: ``if and only if'' means that if the first part is true, then so is the second; and if the second part is true, so is the first. Hence the sentence above is equivalent to both of the following two sentences:
- If two lines are parallel then they have the same slope or they are both vertical.
- If two lines have the same slope or they are both vertical, then they are parallel.
Two lines are perpendicular if and only if either the product of their slopes is -1, or if one is vertical and the other horizonal (like the coordinate axes).
Equations of lines:
Point-slope form of a line: The equation of a line is given by
or
where m is the slope of the line, and 
is a point on the line.
slope-intercept form:
where b is the y-intercept of the line.
special lines:
- vertical lines: x=k, where the point (k,0) is on the line.
- horizontal lines: y=k, where the point (0,k) is on the line.
- A line through the origin: y=mx (since b, the y-intercept, is zero).
The slope of a horizonal line is 0, whereas the slope of a vertical line is undefined.
The symbol 
means ``is approximately equal to''.
If you think that equations and properties of lines are easy concepts, great! In spite of their simplicity, the lines (representing linear functions) are incredibly powerful and useful in even advanced mathematics, because they can often provide good approximations to more complicated functions.
The concept of slope is fundamentally important in differential calculus, and is perhaps best thought of as ``rise over run'' (representing the change in y over the change in x).
Pay special attention to the special cases, vertical and horizontal lines: each has an important role to play in differential calculus. They correspond to extreme behavior: either lazy lines, which just lie there neither increasing nor decreasing (horizonal), or lines that rise so steeply/sharply that they stand above a single point on the x-axis!