2.2.1 Equations of Lines - Part I
 in section 1.4, we discussed linear functions
 functions whose symbolic representation is of the form:
f(x) = mx + b
 another form of the same function is:
y = mx + b
 we can refer to this as the equation of a line or a linear
equation
 a linear equation can appear in other forms, e.g.:
3x + 2y = 6
 here, “y is a function of x”, as defined before
 a way to think about the graph of a linear equation:
a graph of all points that satisfy the equation
Parallel and perpendicular lines
Term
Picture
Property
1
Negative reciprocal of x = - x
a
b
Negative reciprocal of b = - a
2.2.1-1
Forms of the Equation of a Line
 given the slope m and the y-intercept b of a line
 you can write its equation in:
slope-intercept form:
y
=
mx +
b


slope
y-intercept
 given a point (x1, y1) on a line and its slope m
 you can write its equation in:
point-slope form:
y = m(x
-
x1) + y1

slope
point: (x1, y1)
Seven Skills
1.
2.
3.
4.
Given:
any linear equation
two points
equation of line
point and slope
5. two points
6. point and line
7. point and line
Find:
its slope-intercept form
slope of line through them
slope of line
equation of line through given
point with given slope
equation of line through them
equation of line through given
point parallel to given line
equation of line through given
point perpendicular to given line
2.2.1-2