1. Slope
Created by Charlean Mullikin:
ML sections 3.6/3.7

2. Slope is the relationship of the
What is it?
Slope is the relationship of the
rise to the run of a line.
m = rise = y2 – y1
run x2 – x1
rise
run

3. Slope can be
positive:
+ ÷ + or - ÷ -
Slope can be
negative:
+ ÷ - or - ÷ +

4. y's are the same x's are the same Slope can be 0: Horizontal÷
anything
Horizontal
x's
are
the
same
Slope can be
undefined:
Anything ÷
Vertical

6. ALWAYS SIMPLIFY SLOPES
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 = undefined
m = 1/3
m = 5
m = 5 1/2
m = 5/0
m = 0/6
m = -15/-25
m = 5/2

7. m = rise = y2 – y1 – run x2 – x1 – (x2 , y2) x2 y2 (x1 , y1) x1 y1On
top!!
(x1 , y1) x1 y1
Run On
bottom!!

8. Find the slope of the line that passes through (3, -3)and (0 , 9)
m = rise = y2 – y1 =
run x2 – x1 –
= -12 3 -3 9 – 3
(0 , 9) 9
= -4
Rise On
top!! –
(3 , -3) 3 -3 –
Run On
bottom!!

9. 6/2 = 3
-10/-2 = 5
-24/8 = -3
2/6 = 1/3
9/0 = undefined
0/22 = 0

10. Application Identify rise and run. Which word points to the rise?
3600 feet
Put the rise on top. =
16328 feet
3.1 miles
What is the run?
3.1 x 5280
= ft
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.

11. Slope on a Grid
Rise: +9 +6
Run: +6 +9
Slope: +9 +6
m = 3 2

12. Slope on a Grid
Rise: 0
Run: 7
Slope: 0 7
m = 0 +7

13. Slope on a Grid
Rise: -7
Run: +4
Slope: -7 +4 -7
m = 7 4 +4

14. Slope on a Grid
Rise: -8
Run: 0
Slope: -8 -8
m = undefined

15. YES, Since the slopes are the same (1=1), then the lines ARE PARALLEL.+5
a: m= =1 +5 +5 +2 +2
b: m= =1 +5 +2 +2
YES, Since the slopes are the same (1=1),
then the lines ARE PARALLEL.

16. 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

17. What is the slope of….. 1/2 -2 1/6 -6 3/5 -5/3 -8/7 7/8 No slope 4
Slope of given line
Parallel Line?
Perpendicular Line?
1/2 -6
3/5
-8/7 4
No slope
1/2 -2
1/6 -6
3/5
-5/3
-8/7
7/8
No slope 4
-1/4
No slope

18. Writing Equations
Shortcut #1 1

19. Writing Equations
Shortcut #2 1

20. Writing Equations

21. Writing Equations
Shortcut #1
Shortcut #2

22. Writing Equations

23. 1 1

24. Identify ONE point to use
Find slope
Substitute

25. Simplify and solve for y
Distributive
Property of =
Addition Property of =
(Add 8 to both sides)
Combine like terms
Use calculator!

26. 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

27. 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

28. 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 (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

29. 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

30. 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

31. 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