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1.3
Lines
Slope of a Line
Given two points (x1,y1) and (x2,y2), the slope of the line passing through
these points is given by
m
y2  y1 y1  y2 rise


x2  x1 x1  x2
run
Example: Find the slope of the line passing through the two points.
a)
(1,3) and (7,5)
b) (-5,-2) and (5,-4)
c) (2,3) and (-5,3)
d) (2,7) and (2,-3)
The General Form of a Linear Equation
ax + by = c
Slope-Intercept Form
y = mx + b
Example: Find the general form of the equation of the line with slope 4 and
y-intercept (0,-2).
Point-Slope Form
y - y1 = m(x - x1)
Example: Write the slope-intercept form of the equation of the line with
slope -2 passing through the point (5,-6).
Example: Write the general form of the equation of the line passing
through the points (1,3) and (7,5).
Example: Write the equation of the line passing through the points (2,7)
and (2,-3).
Example: Write the equation of the line passing through the points (2,3)
and (-5,3).
Parallel and Perpendicular Lines
If two lines are parallel, there slopes are the same. If two lines are
perpendicular, there slopes are negative reciprocals.
Example: Write the equation of the line passing through the point (3,5)
which is perpendicular to the line 2x + 6y = 7.
Example: Graph
3x + 4y = 12 using intercepts.