Straight Lines
Straightline equations are those that are first
degree in both x and y.
Slope: the measure of “steepness”
of a line. Two points on the line are needed to determine the
slope.
where (x_{1}, y_{1}) and (x_{2},
y_{2}) are the coordinates of any two points on the line
Line Equations:
PointSlope Form: 
y  y_{1 }= m(x  x_{1})
where (x_{1}, y_{1}) is the point and m
is the slope 
Need a point and the slope to use this
form 
SlopeIntercept Form: 
y = mx + b where m is the slope and b is
the yintercept (0,b) 
Need a slope and a point on the line, OR
Need the slope and yintercept 
* Equations must be in the slopeintercept form (solved for y
) in order to easily “see” what the slope and y
intercept are.
Parallel Lines… have the same slopes and
different yintercepts
Perpendicular Lines… have slopes that
are negative reciprocals. If the slope of one line is 4 , then
the slope of the perpendicular line is .
Graphing Linear Equations:
 Find the x intercept by letting y = 0, then find the y
intercept by letting x = 0. Plot these two points, and
draw the line that connects the two points.
 If the equation is given in slopeintercept form: Plot
the y intercept first. From the y intercept, use the
slope information to go up/down, then right, to obtain
another point. Connect these two points, and you have
graphed the line.
Vertical Lines… are missing the y
variable. The slope of a vertical line is undefined. x = 3 is the
equation of a vertical line, where the x coordinate is always 3,
and the y coordinate can be any value.
Horizontal Lines… are missing the x
variable. The slope of a horizontal line is zero. y = 2 is the
equation of a horizontal line, where the y coordinate is always
2, and the x coordinate can be any value.
Horizontal and Vertical lines are perpendicular.
