Advanced Geometry

1

• Advanced Geometry
• Parallel and Perpendicular Lines
• Lesson 2

Slopes and Equations of Lines
2
Slope
Point 1 and Point 2
Slope can also be called a rate of change.

3
Find the slope of each line.
, if A(-3, 7) and B(-1, -1)
4
Find the slope of each line.
5
Special Cases
Horizontal Line (flat) m 0
Vertical Line (up and down) m undefined

6
For one manufacturer of camping equipment,
between 1995 and 2005 annual sales increased
by 7.4 million per year. In 2005, the total
sales were 85.9 million. If sales increase at
the same rate, what will be the total sales in
2015?
7
Parallel and Perpendicular Slopes
Perpendicular lines have slopes that are
negative reciprocals.
Parallel lines have exactly the same slope.

• different signs
• flip the fraction

• same sign
• same numbers in
• the same places

8
Determine whether
and
are parallel, perpendicular, or neither. F(-2,
-5), G(4, 7), H(0, 2), J(8, -2)
9
Determine whether
and
are parallel, perpendicular, or neither. F(4,
2), G(6, -3), H(-1, 5), J(-3, 10)
10
Determine whether
and
are parallel, perpendicular, or neither. F(1,
-3), G(-2, -1), H(5, 0), J(6, 3)
11
Graph the line that contains Q(5, 1) and
is parallel to with M(-2, 4) and N(2,
1).
12

Graph the line that contains A(0, 1) and
is perpendicular to with X(-6, -2) and
Y(0, -6).
13
Equations of Lines
Slope-Intercept Form
y mx b
m slope
b y-intercept
Write an equation in slope-intercept form
of the line with slope of -6 and y-intercept of
(0, -2).
14
Equations of Lines
Point-slope Form
m slope
Write an equation in point-slope form of the
line whose slope is
that contains (-10, 8).
15
Write an equation in slope-intercept form
for a line containing (4, 9) and (-2, 0).
16
Write an equation in slope-intercept form
for a line containing (1, 7) that is
perpendicular to the line y
x 1.