1. SLOPE
SECTION 3-3
Spi.2.1.D
Jim Smith JCHS

2. The Slope Of A Line Is The Ratio Of The Vertical Rise To The Horizontal Run

3. Let’s move from point A to point B
Let’s move from point A to point B. We’ll take the elevator down 9 floors. (down is negative) Then we’ll run right, across the hall 9 spaces. ( right is positive) We end up with the rise = run 9 A
SLOPE = -9 = -1 9 -9 B 9

4. D C Now move from D to C Down 3 (neg) Left 8 (neg) Rise = -3 = 3
Let’s move from C to D.
Move up 3. (Up is positive) Move right 8.
Rise = 3
Run 8
Now move from D to C
Down 3 (neg)
Left 8 (neg)
Rise = -3 = 3
Run 8 D 3 -3 C -8

5. RISE = Y1 – Y2 RUN X1 – X2 Think …”The rise is the Y’s”
The slope of a line is the RISE
RUN
Think …”The rise is the Y’s”
RISE = Y1 – Y2
RUN X1 – X2
Y’s on top. It doesn’t matter which Y goes first.
Just start with the X from the same pair.

6. Find The Slope Of The Line Through:
(3,6) and (-4,7)
6-7 = -1 =_ 1
3-(-4)
(4,8) and (9,2)
8-2 = 6 = _ 6
(-3,-7) and (-9,-1)
(-7)-(-1) = -6 = -1
(-3)-(-9)
(12,9) and (6,0)
9-0 = 9 = 3

7. If You Read A Line From Left To Right And It
Goes Uphill, It Has A Positive Slope. Downhill
Means A Negative Slope.
pos
neg

8. There are 2 special cases. A vertical line
has an undefined slope. That means the x’s
are equal so we get a 0 in the bottom of our
fraction (ex. 5/0). A horizontal line has a
slope of zero. The y’s are equal so the 0 is
in the top of the ratio ( ex. 0/4). Remember
horizontal and zero both have a Z .

9. ¼ and ¼ ½ and -2 Parallel lines Perpendicular lines
PARALLEL or PERPENDICULAR
Parallel Lines Have The Same Slope.
Perpendicular Lines Have Slopes That Are
Opposites And Reciprocals
Parallel lines
Slopes
¼ and ¼
Perpendicular lines
Slopes
½ and -2

10. Are AB and CD parallel, perpendicular
or neither?
A(-2,-5), B(4,7), C(0,2), D(8,-2)
Slope of AB =
-5 – 7
-2 – 4 =
-12 -6
= 2
Opposites and
reciprocals
Slope of CD =
-2 - 2
8 - 0 = -4 8
_ 1 2
PERPENDICULAR

11. Are AB and CD parallel, perpendicular
or neither?
A(4,3), B(5,2), C(0,0), D(5,1)
Slope of AB =
3 - 2
4 - 5 = 1 -1
ARE THE SLOPES
THE SAME ?
OPP and RECIP ?
NEITHER
Slope of CD =
1 - 0
5 - 0 = 1 5

12. Graph the line with a slope of 3 and passes
Through (2,1)
Slope = 3 = 3 1
3 also = -3 -1
(2,1)

13. -1 4 First find the slope CT Slopes of Perpendicular lines are
Graph the line that passes through ( 3,2 ) and
is perpendicular to CT with C( 2,2 ) , T( 4,10 )
First find the slope CT
Slope of CT = =
= 4 or 4 1
Slopes of Perpendicular lines are
opposites and reciprocals
Slope of new line = -1 4

14. Slope -1/4 Passes through ( 3 ,2 )