1. SLOPE AND
PARALLEL AND
PERPENDICULAR LINES

2. You will need the worksheet that goes along
with this power point presentation, a pencil, a
ruler, and a piece of graph paper. Read
and follow directions carefully. At the end of
The presentation, you should know something
about the slopes of parallel lines and the
slopes of perpendicular lines.

3. REVIEW: Parallel lines (//) are lines that never intersect.
Perpendicular lines () are lines that intersect to form
right angles.

4. SLOPE
One nice thing about slope is that it’s a concept you already know about
from everyday life. People talk about the slope of hills; golf commentators
discuss the gentle slope of putting greens. So experience tells you that
slope has to do with steepness. In math, slope has a specific, technical
meaning:
It means the steepness of lines on the coordinate plane.
From life, you also have a sense of what steepness means. For example,
after climbing two hills, you should be able to say which one was steeper
(at least your leg muscles will tell you the next day). But math, exact
science that it is, allows you to measure steepness with perfect, numerical
precision.

5. In algebra, the symbol for slope is the letter m. Here are
some other things to know about slope:
• A horizontal line, having no steepness,
has a slope of 0.
• A vertical line, having absolute steepness,
has a slope that is undefined.
• Lines that rise from left to right have a
positive slope.
• Lines that fall from left to right have a
negative slope.

6. What is the formuula for the slope of a line? OR
The formula for the slope of a line is:
rise
y2 - y1 OR
m =
m =
run
x2 - x1
where (x1, y1) and (x2, y2)
are the coordinates of any
two points on the line.
(x2, y2)
(x1, y1)

7. Find the slope of the lines passing through these points.
Show your work and write your answers on your piece of
paper (#6).
a) (4, 3) and (9, 6)
b) (8, -2) and (6, 5)
- 3
= 3/5
= -7/2
c) (-10, 5) and (15, -20)
d) (-3, -6) and (8, 7)

8. Count the slope when you are given a line on a graph.
To get from one point to the other on the line, you have to go up 2 and over 3 to the right,
so the slope is ⅔.
Over 3
Up 2

9. Find the slope of the line graphed below.
Notice that to get from
one point to the next on
this graph you have to
go down 2 and to the
right one, so the slope
is -2/1.

10. If you are given a point on a line and the slope of the line, you
can graph the line.
• Graph the point that you are given.
This will be the starting point.
• Start at the point you graphed and
count the slope.
Graph the line through (-6, -5)
with slope 3/2.

11. The line through (-4, 2) with slope of 4/5.
Use the graph by #7 on your worksheet to complete the
following graphs:
The line through (-4, 2) with slope of 4/5.
b) The line through (1, 2) with slope of -3/4.
c) The line through (3, -2) with slope of 3.

12. On your graph for #8, graph the line through (2, 3) with a slope of ¾.
On the same graph, graph the equation y = ¾ x + -4.
Click here if you need
to review how to graph
a linear equation.
What do you notice about the two lines that you graphed?
What do you notice about the slopes of the two lines?

13. On the graph for #9, graph AB and CD.
Click here if you
forgot how to
find slope.
Find the slope of each line.
The slope of AB = 6/5 5/6 -5/6 -6/5
The slope of CD = 6/5 5/6 -5/6 -6/5
Click on the correct answer.
What do you notice about the two lines that you graphed?
What do you notice about the slopes of the two lines?

14. What can you conclude about the slopes of parallel lines?
The slopes of parallel lines are equal or the same!!
The slope of a line is 1/3. What is the slope of a line
parallel to this one? 3
-1/3
1/4
1/3

15. Line b has a slope of 2/3 and line d has a slope of 1/3. Is b // d?
yes no
E (2, -11), F (4, -5), G (2, 8) and H (5, 17)
Without graphing, determine if EF// GH.
Show all work on your paper next to #10. (think slope)
Click here if you forgot
how to find slope.

16. Graph the line through (-5, -8) with a slope of ½. (Do this on
the graph for #11).
On the same graph, graph the line that passes through (-9, 7)
with a slope of -2.
What do you notice about the two lines?
Is there a relationship between the slopes?

17. Graph the two equations below on the graph for #12.
y = 2/3 x + 2
Click here if you need
help graphing linear
equations.
y = -3/2 x + -3
What do you notice about the two lines?
What do you notice about the slopes? (Hint: try multiplying
them)

18. What do you notice about the two lines?
L (-4, 0) M (0, 3) N (1, 7) P (4, 3)
Graph LM and NP on #13.
What do you notice about the two lines?
Click on the slope of LM : ¾ 4/3 -3/4 -4/3
Click on the slope of NP : ¾ 4/3 -3/4 -4/3
What do you notice about the slopes of these two
perpendicular lines? Hint: try multiplying them again.
Click here if you forgot
how to find slope.

19. What can you conclude about the slopes of perpendicular lines?
The product of the slopes of perpendicular lines is -1.
Notice that if the slope of the original line is ¾, to find the
slope of the perpendicular line (-4/3) you flip the original
slope (reciprocal) and make it the opposite.
The slope of a line is -5/7. What is the slope of the
perpendicular line? (flip and opposite)
5/7 7/5 -5/7 -7/5

20. Line a has a slope of -1/2 and line c has a slope of 2. Is a  b?
yes no
Q (-3, -2) R (9, 1) S (3, 6) T (5, -2)
Without graphing, determine if QR  ST. Think slope.
Show all work on your paper next to #14.
Click here if you forgot
how to find slope!

21. Slopes of parallel and perpendicular lines
The equation for a line is y = ¼ x + 5.
What is the slope of a line parallel to this one?
¼ /1 -1/ / /1
What is the slope of a line perpendicular to this one?
¼ /1 -1/ / /1

22. Complete #15 & #16
on your worksheet.
Did you complete #15 & #16?

23. Okay, I get it! The slopes of parallel lines are equal!
And the slopes
of perpendicular
lines are opposite
reciprocals (their
product is -1)!
For perpendicular
lines I just flip the
slope and change
to its opposite.
That’s what I said!

24. Complete #17 & #18
on the worksheet
and then you are
finished!

25. CORRECT!

26. Try again.

27. Review - graphing a linear equation:
To graph the equation y = ½ x + 2:
1. Graph the y-intercept (the point where the line
crosses the y-axis) - (0,2)
Count the slope - rise over run
(½)
Draw a line through
the points
Return to previous slide

28. Try Again.
Remember that the slopes of parallel lines are equal.

29. Try Again. Remember that the slopes of perpendicular lines
have a product of -1. So, take the original slope and
flip it. Then make it the opposite.

30. Return to previous slide.
What is the formuula
for the
slope of a line?
The formula for the slope of a line is:
rise
y2 - y1 OR
m =
m =
run
x2 - x1
where (x1, y1) and (x2, y2)
are the coordinates of any
two points on the line.
(x2, y2)
(x1, y1)
Return to previous slide.

31. The
End