Transcript 8.EE.5 I can statements #1

Objective
The student will be able to:
• Determine the slope of a line between
2 points, on a graph, and in an
equation.
• Compare the slopes of two different
lines.
Career Focus
Mathematics is used by architects to express the design images on a
drawing that can then be used by construction workers to build that
image for everyone to see. Mathematics is needed to analyze and
calculate structural problems in order to engineer a solution that will
assure that a structure will remain standing and stable. The sizes and
shapes of the elements of a design are possible to describe because
of mathematical principles such as slope, linear lines, area, and
perimeter.
Activating Strategy
What is the meaning of this sign?
1.
2.
3.
4.
Icy Road Ahead
Steep Road Ahead
Curvy Road Ahead
Trucks Entering
Highway Ahead
What does the 7% mean?
7% is the slope of the road.
It means the road drops 7 feet
vertically for every 100 feet
horizontally.
7%
7 feet
100 feet
So, what is slope???
Slope is the steepness of a line.
Slope can be expressed different ways:
( y2  y1 ) rise
vertical change
m


( x2  x1 ) run horizontal change
A line has a positive slope if it is
going uphill from left to right.
A line has a negative slope if it is
going downhill from left to right.
Slope Intercept Form
Y =MX + B
Ex.) Slope can be easily identified as “m”
1.Y = 4x + 2
2.Y = 1/5x + 5
3.Y = 2x + 5
1) Determine the slope of the line.
When given the graph, it is easier to apply
“rise over run”.
Determine the slope of the line.
Start with the lower point and count how
much you rise and run to get to the other
point!
6
3
rise
3
1
=
=
run
6
2
Notice the slope is positive
AND the line increases!
2) Find the slope of the line that passes
through the points (-2, -2) and (4, 1).
When given points, it is easier to use the formula!
( y2  y1 )
m
( x2  x1 )
y2 is the y coordinate of the 2nd ordered pair (y2 = 1)
y1 is the y coordinate of the 1st ordered pair (y1 = -2)
(1  (2)) (1  2) 3 1
m

 
(4  (2)) (4  2) 6 2
Did you notice that Example #1 and
Example #2 were the same problem
written differently?
6
3
(-2, -2) and (4, 1)
1
slope 
2
You can do the problems either way!
Which one do you think is easiest?
AP #1: Find the slope of the line that
passes through (3, 5) and (-1, 4).
1.
2.
3.
4.
4
-4
¼
-¼
Find the slope of the line that goes
through the points (-5, 3) and (2, 1).
y2 - y1
m=
x2 - x1
1 3
m
25
1 3
m
2  (5)
2
m
7
Determine the slope of the line shown.
1.
2.
3.
4.
-2
-½
½
2
Determine the slope of the line.
-1
2
Find points on the graph.
Use two of them and
apply rise over run.
rise 2
=
= -2
run -1
The line is decreasing (slope is negative).
What is the slope of a horizontal line?
The line doesn’t rise!
0
m=
=0
number
All horizontal lines have a slope of 0.
What is the slope of a vertical line?
The line doesn’t run!
number
m=
= undefined
0
All vertical lines have an undefined slope.
Remember the word
“VUXHOY”
Vertical lines
Undefined slope
X = number; This is the equation of the line.
Horizontal lines
O - zero is the slope
Y = number; This is the equation of the line.
Comparing the slopes of 2 lines
• Sometimes, you will have to compare the
slopes of two lines, and they may be in
different forms.
Ex.) an equation and a graph
• The greater slope will be the steeper line
Comparing the slopes of 2 lines
1
Which line is steeper?
The graph or the equation?
3
Y = (1/4)X+ 2
AP #2: Which line is steeper?
Graph:
Line between 2 points:
(–2, –7) and (3, 8)
AP #2: Which line is steeper?
Line Z that passes through points (-1, -8) and (4, 7)
or Line J that passes through (2, 3) and (5, 9).
Which line is steeper?
Look at the following 2 graphs. Explain your
answer in 1 complete sentence.
Real-Life Scenario
• Franklin is an architect. He wants to build a
house so his elderly grandpa can easily
travel up and down the stairs. The following
equation and points represent two possible
slopes for the staircase. Which one should
Franklin choose to build and explain why.
Y = 5x +2
(3, 5) (4, 7)
Now, I can…
Determine the slope of an equation
Determine the slope of a graph between 2
points
Compare 2 different slopes
Determine which slope is the steepest
Identify horizontal and vertical lines
Reason how to use slope in a real world
scenario