Standard Form Linear Equation

Ax+By+C=0

"A" and "B" are both coefficients of x and y. "C" is a constant term (just a number).

application: Solve for y:
Ax+By+C=0
By=-Ax-C
y=(-Ax/B)-(C/B)

y=mx+b
Therefore we see that m=-A/B and b=-C/B

Parallels and Perpenducilars

Parallel - two lines (rays, segments) are parallel if they are COPLANAR and EQUIDISTANT throughout their length.

Coplanar - A set of points is said to be coplanar if and only if they lie on the same geometric plane.
Equidistant - Equally distant. For example, any two points on a circle are equidistant from the center.

Perpendicular - two lines (rays, segments) are perpendicular if they are COPLANAR and Intersect at a 90 "degree" angle.

Point Slope Form

y-y1=m(x-x1)

Where m=slope & (x1,y1) corresponds to specific points on the coordinate
example: Consider the line 2x+3 and write its equation in point slope form
Graph the line: y=2x+3
Slope=2
Y-Intercept=3
x__________y
-1_________1
0__________+3
-2_________-1


y-y1=m(x-x1)
y-1=2(x-(-1)) or in simplified form y-1=2(x+1)
OR
y-3=2(x-0) or in simplified form y-3=2x
OR
y-1=2(x-(-2)) or in simplified form y+1=2(x+2)

Slope y-Intercept Form

y = mx + b
m is slope and b is y-intercept.

ex) Write the slope y-intercept form for the points (-2, 1) and (4, 4).

First find slope
= (y2 - y1)/(x2 - x1)
= (4 - 1)/(4 - (-2))
= 3/6
= 0.5 or 1/2

Now that we have a y-coordinate, the slope and an x-coordinate we can find the y-intercept.
b = y - mx
b = 4 - .5(4)
b = 4 - 2
b = 2

y = 0.5x + 2

http://www.gomath.com/exercises/SlopeEquationYintercept.php
http://www.learningwave.com/lwonline/algebra_section2/yintercept2.html
http://en.wikipedia.org/wiki/Linear_equation

Midpoint

Midpoint - A point on a line segment that divides the segment into two congruent segments. A point that is exactly half way between two set points.

http://library.thinkquest.org/20991/geo/coordgeo.html#distance

Distance

Distance - In the mathematical subfield of graph theory we can define a notion of distance between two vertices in a graph. The extent or account of space between two objects or points.

Find the distance between
A(-2, 3) and B(8, -1).

d = SQRT[(8 - (-2))^2 + (-1 - 3)^2]

Simplify.

d = SQRT[(10)^2 + (-4)^2]
d = SQRT(100 + 16)
d = SQRT(116)
d = 10.77units



http://library.thinkquest.org/20991/geo/coordgeo.html#distance

Slope

Slope - In mathematics, the slope of a straight line (within a Cartesian coordinate system) is a measure for the "steepness" of said line. With an understanding of algebra and geometry, one can calculate the slope of a straight line; with calculus, one can calculate the slope of the tangent to a curve at a point.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/int_algebra/int_alg_tut15_slope.htm

Table of Values