Created by Charlean Mullikin: mullikinc@anderson3.k12.sc.us
ML sections 3.6/3.7
Slope is the relationship of the
rise to the run of a line.
m = rise = y2 – y1
run
x2 – x1
Slope can be
positive:
Slope can be
negative:
+ ÷ + or - ÷ -
+ ÷ - or - ÷ +
Slope can be
0:
0
÷
Horizontal
Slope can be
undefined:
Vertical
anything
Anything
÷
0
m = -4
ALWAYS SIMPLIFY
SLOPES
m = 12/-8
m = 15/3
m = - 3/5
Slopes are positive, negative, 0, or Undefined (No slope).
Slopes are written as integers with one sign, proper
fractions, or improper fractions (no mixed fractions).
When 0 is on top, the slope is 0.
m=0
m = -5/-3
When 0 is on bottom, the slope is undefined or no slope.
m=5
m = 0/6
m = 1/3
m = 5 1/2
m = -15/-25
m = undefined
m = 5/0
m = 5/2
m = rise = y2 – y1
run
x2 – x 1
(x
x2 , y2)
Rise
On
top!!
x1 , y1)
(x
Run On
bottom!!
Find the slope of the line that passes through (3, -3)and (0 , 9)
m = rise = y2 – y1 =
run
x2 – x1
-3 – 9
3
–0
= -12
=
(0
0, 9
9)
Rise
On
top!!
–
(3
3 , -3
-3)
–
Run On
bottom!!
3
-4
a: m=
+5
+2
+5
+5
+5
b: m=
=1
+2
+2
+2
YES, Since the slopes are the same (1=1),
then the lines ARE PARALLEL.
=1
6/2 = 3
-10/-2 = 5
-24/8 = -3
2/6 = 1/3
9/0 = undefined
0/22 = 0
Application
Identify rise and run.
Which word points to the rise?
3600 feet
16328
3.1 miles
feet
3.1 x 5280
= 16368 ft
=
Put the rise on top.
What is the run?
Put the run on bottom.
The average slope is about .22.
Change to same units, then Divide out and
Answer the question in reasonable units.
Perpendicular Lines
 When
two lines are perpendicular,
there are two cases with relation to
slopes:
 Case 1-If neither line is vertical, the
product of the two slopes is negative
one (Opposite reciprocals).
m1=2/3 and m2= - 3/2
 Case 2 – If one of the lines is
vertical, then the perpendicular line
is horizontal.
m1=undefined and m2= 0
What is the slope of…..
Slope of given line
Parallel Line?
Perpendicular Line?
1/2
1/2
-2
-6
-6
1/6
3/5
3/5
-5/3
-8/7
-8/7
7/8
0
0
No slope
4
4
-1/4
No slope
No slope
0
Writing Equations
Shortcut #1
1
Writing Equations
Shortcut #2
1
Writing Equations
Writing Equations
Shortcut #1
Shortcut #2
Writing Equations
1
1
Find slope
Identify ONE point to use
Substitute
Simplify and solve for y
Distributive
Property of =
Addition Property of =
(Add 8 to both sides)
Combine like terms
Use calculator!
Parallel Equations
 Lines
that are parallel have the same
slope.
– Identify slope of given line
– Identify point parallel line passes
through
– Use point-slope equation to write
equation
Parallel Equations

Write the equation of the line parallel
to y = ¾ x – 5 that passes through
the point (3, -2).
m = ¾, parallel slope is also ¾
Point (3, -2)
y – y1 = m(x – x1)
y - -2 = ¾(x – 3)
y + 2 = ¾ x – 9/4
y = ¾ x – 9/4 – 2
y = ¾ x – 17/4
Parallel Equations

Write the equation of the line parallel to
7x + 5y = 13 that passes through the point
(1, 2).
 Solve for y to find slope:




7x + 5y = 13
5y = -7x + 13
(subtract 7x from both sides)
y = -7/5 x + 13/5 (Divide each term by 5)
parallel slope is – 7/5
 Point (1, 2)
 y – y1 = m(x – x1)
 y - 2 = - 7/5 (x – 1)
 y - 2 = -7/5 x + 7/5
 y = -7/5 x + 7/5 + 2
 y = -7/5 x + 17/5
Perpendicular Equations
 Lines
that are perpendicular have
slopes that multiply to equal -1. They
are opposite sign, reciprocal
numbers.
– Identify slope of given line
– Change the sign and flip the number to
get the perpendicular slope.
– Use point-slope equation to write
equation
Perpendicular Equations

Write the equation of the line perpendicular to
7x + 5y = 13 that passes through the point
(1, 2).
 Solve for y to find slope:




7x + 5y = 13
5y = -7x + 13
y = -7/5 x + 13/5
perpendicular slope is +5/7
 Point (1, 2)
 y – y1 = m (x – x1)
 y - 2 = +5/7(x – 1)
 y - 2 = 5/7 x – 5/7
 y = 5/7 x – 5/7 + 2
 y = 5/7 x + 9/7
Perpendicular Equations

Write the equation of the line
perpendicular to y = ¾ x – 5 that
passes through the point (3, -2).
m = ¾, perpendicular slope is – 4/3
Point (3, -2)
y – y1 = m(x – x1)
y - -2 = -4/3(x – 3)
y + 2 = -4/3 x + 4
y = -4/3 x + 4 – 2
y = -4/3 x + 2