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LINES
I. Rectangular Coordinate System
Developed by Rene Descarte in the 1500’s for the purpose of visualizing
concepts in algebra. This coordinate system has an x-axis and a y-axis, which
divide the plane into four quadrants. Each position in the plane is
determined using an ordered pair ( x, y ) where x gives the horizontal position
and y gives the vertical position. The only formula in this section is the
 x  x2 y1  y 2 
midpoint formula M   1
,
.
2 
 2
II. Graphing linear equations
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Tables of ordered pairs
Intercept method
x-intercept: Set y=0 and solve for x.
y-intercept: Set x=0 and solve for y.
III. Slope
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Geometrically, slope is a measure of the steepness of a line.
Algebraically, slope is a measure of the average rate of change.
y  y1
The formula for slope is m  2
.
x 2  x1
Sketch lines with positive, negative, zero and undefined slopes.
Parallel lines have the same slope m2  m1 .
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The slopes of perpendicular lines are negative reciprocals m2 
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IV. Equations of lines
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Slope-intercept from for the equation for a line y  mx  b
Point-slope form for the equation of a line y  y1  m( x  x1 )
Horizontal lines y  constant
Vertical lines x  constant
1
.
m1
V. Functions
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A function is a rule, which maps each x to a unique y.
Vertical line test: A vertical line intersects the graph of a function at most
once.
Function notation. Evaluate functions by substitution.
The domain is the set of all the allowable inputs or x-values.
The range is the set of all the allowable outputs or y-values.
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