• Why did the girl wear
glasses during math
class?
Why was six afraid of seven?
What is slope? When is it used? How
can it be found?
Finding slope
• Find the slope for the
following
• Joy rides her bike 5
miles per hour.
• (0,0)(1,5)
• (2,6)(-3,5)
• Y=2x+7
• Y=-3x +4
•
•
•
•
•
5/1
5/1
1/5
2
-3
Slope fomula (y1 - y)/(x1- x )
• Slope formula measures
the rise divided by the
run.
• Find the rise by
subtracting y
coordinates of 2 points
on a line.
• Find the run by
subtracting the x
coordinates of 2 points
on a line
• Example
• (3,8) (7,-1)
• Change in y 8 - -1 = 9
• Change in x 3 – 7 = -4
• 9/-4 is the slope
Slope with formula and slope triangle
• Example
• (3,8) (7,-1)
• Change in y is 8 - -1 = 9
• Change in x is 3 – 7 = -4
• 9/-4 is the slope
Determine if the following lines are
translations
• Line a (2,3)(4,5)
• Line b (2, 4)(4,6)
• Y=2x+5
• Y=2x +2
When would it be important to
determine if two lines are parallel
Given two points on two lines
determine if the lines are parallel.
• (0,0)(1,2)
• (0,3)(1,5)
• Are the slopes the
same?
• Is one a translation of
the other?
Given two points on two lines
determine if the lines are parallel.
• (3,-1)(5,3)
• (-1,3)(1,6)
• Are the slopes the
same?
• Is one a translation of
the other?
Given two linear equations can you
determine if they are parallel?
• Y=2/3x +4
• Y= 2/3x +1
• Are the slopes the
same?
• Is one a translation of
the other?
Parallel lines
In 2008 the snowpack
melted from the mountains
at 7 inches per week The
beginning snow pack was
100 inches.
In 2010 The snowpack
melted from the mountains
at 7 inches per week. The
beginning snow pack was
110 inches.
Explain how the graphs of
these two situations would
compare to each other.
Perpendicular lines
• Perpendicular lines
have slopes that are
opposite reciprocals.
• Slope 2/3
• Slope -3/2
• Think of the two
triangles as a 90 degree
rotation.
Perpendicular lines
• Which of the following
lines are perpendicular?
• Which of the following
lines are parallel?
• Which of the following
lines are neither?
Line a
Line b
Problem 1
Y=2x+4
Y=-2x+3
Problem 2
Y= -3x+1
Y= -1/3x +2
Problem 3
Y= 5x +3
Y= -1/5x +1
Problem 4
Y= 3/4x+2
Y=3/4x -2
Problem 5
Y= -2/3x +1
Y=3/2x -1
Problem 6
2x+y = 8
X- 2y =12
Perpendicular lines
Are the two lines
represented by the
following points going to
be perpendicular parallel
or neither?
Line a
Line b
Example
(2,5)(-2,7)
(3,6)(4,8)
𝑦1−𝑦2
5−7
2 − −2
6−8
3−4
M=𝑥
1 −𝑥2
−2 −1
=
4
2
−2
−1
2
=1
Problem 2
(3,1)(6,2)
(5, 3)(11,5)
Problem 3
(5,-2)(6,6)
(4,-5)(5,1)
Problem 4
(0,0)(3,4)
(1,1) ( 5,-4)
Problem 5
(20,16)(8,4)
(2,2)(-3,3)
Perpendicular lines that are vertical
and horizontal
• Are the following pairs
of lines perpendicar?
• What is the equation
for both lines?
• What general rule can
we come up wit hfor
this situation?
Find a line that goes through a given
point and is parallel to a given line.
• Find a line that goes
through the point (1,6)
and is parallel to y=2x+1
• 1. Slope of the line is 2
• 2. Fill in numbers for m,x
and y
y=mx+b 6 = 2(1)+b
• 3. Solve for b. b=4
• 4 Write your new
equation with m and b
• y= 2x+4
Find a line that goes through a given
point and is perpendicular to a given
line.
• Find a line that goes
through the point (1,6) and
is perpendicular to y=2x+1
• 1. Slope of the line is -1/2
• 2. Fill in numbers for m,x
and y
y=mx+b 6 = -1/2(1)+b
• 3. Solve for b. b=6.5
• 4 Write your new equation
with m and b
• y= -1/2x+6.5
Quiz
• 1. Find slope
• A. (2,6) (4, -4)
• B. (-4,5) (7, -3)
• 2. Are the lines a
translation
• (2,5) (5,12)
• (-4,3) (-1,10)
• 3. Determine if the
lines are parallel
perpendicular or
neither
• Y=2x+3, y= -1/2x -4
• Y=-2/6x +1 y= -1/3x +4
• Y = 5x
y = 1/5x
When would it be important to find
the distance from a point to a line?
• When you are riding a
thirsty horse in the
desert and you need to
get to a river.
When would it be important to find
the distance from a point to a line?
• When you are putting a
sprinkler line together
and you need to know
the distance from the
line to the sprinkler
hook up
When would it be important to find
the distance from a point to a line?
• When you are trying to
figure out the altitude
of a triangle on a
coordinate plane.
• Altitude can help you
find the area of a
triangle.
Find the distance from a point to a line
• 1. graph the point and the
line
• 2. Determine the
equation of a line
perpendicular to the line
running through the
point.
• 3. Use substitution to
determine the
intersection of 2 lines.
• Use distance formula to
measure the distance
from the point to the line.
• Y=2x+3 (2,2)
• 2=-1/2(2)+b
2= -1+b
3=b
Y=-1/2x+3
• 2x+3= -1/2x+3
x=0 y=3
• Find distance from (0,3)
to (2,2) = sqrt 5