finding the slope of a line. what is the meaning of this sign? 1.icy road ahead 2.steep road ahead...
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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% So, what is slope??? Slope is the steepness of a line. 7 feet 100 feet Just copy this definitionTRANSCRIPT
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Finding The Slope of a Line
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What is the meaning of this sign?
1. Icy Road Ahead2. Steep Road Ahead3. Curvy Road Ahead4. Trucks Entering
Highway Ahead
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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%
So, what is slope???Slope is the steepness of a line.
7 feet
100 feetJust copy this definition
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Slope can be expressed different ways:
A line has a positive slope if it is going uphill from left to right.
A line has a negative slope if it isgoing downhill from left to right.
2 1
2 1
( ) vertical change( ) horizontal changey y risemx x run
Copy this slide
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Finding the slope of a line
on a graph
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Graph (3, 2) and (-1, -1)
Just watch
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Draw a line through the points.
Just watch
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Now that we have our line lets find its slope.
Remember we are finding the following ratio:
Vertical or Rise Horizontal Run
Just read
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VERTICAL Changeor the RISE
3
Just watch
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HORIZONTAL Changeor the RUN
4
3
Just watch
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Vertical Rise Horizontal Run
34
Just watch
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When given the graph, it is easier to apply “rise over run”.
Determine the slope of the line.Just watch
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Start with the lower point and count how much you rise and run to get to the other
point!
Determine the slope of the line.
6
3
run36
= =12
rise
Notice the slope is positive AND the line increases!
Just watch
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Determine the slope of the line shown.
1. -22. -½3. ½4. 2
If there are no points on the graph place points on the line at an intersection.
Just watch
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Determine the slope of the line shown.
1. -22. -½3. ½4. 2
If there are no points on the graph place points on the line at an intersection.
2
-1
RiseRun
2-1
Just watch
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Find the slope of these lines
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What is the slope of a horizontal line?
The line doesn’t rise!
m 0
number0
All horizontal lines have a slope of 0.
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What is the slope of a vertical line?
The line doesn’t run!
All vertical lines have an undefined slope.
m number
0undefined
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Remember the word “VUXHOY”
Vertical linesUndefined slopeX = number; This is the equation of the line.Horizontal linesO - zero is the slopeY = number; This is the equation of the line.
Copy in notebook
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Record notes in foldable first under the GRAPH heading.
Partner Work – Pass out worksheet. Find the slopes of the graphs.
Go ahead on slides for finding slopes other ways.
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Finding the slope of a line
when given two points
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Find the slope of the line that passes through the points (-2, -2) and (4, 1).
(1 ( 2))(4 ( 2))
m
2 1
2 1
( )( )y ymx x
(1 2)(4 2)
When given points, it is easier to use the formula!
Label your points.
136 2
y1y2x1
x2
m represents slope
Take Notes!
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Did you notice that Example #1 and Example #2 were the same problem
written differently?
(-2, -2) and (4, 1)6
312
slope
You can do the problems either way!Which one do you think is easiest?
Just watch
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3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).
m y2 y1
x2 x1
1 32 ( 5)
m
1 32 5
m
27
m
y2y1 x2x1
Write formula
Label points
Substitute number for variables.
Take Notes!
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Find the slope of the line that passes through (2, 5) and (3, 6).
1. 22. 13. - 14. -2
1st – Write Formula for finding slope2nd – Label your points3rd – Substitute numbers in for variables.4th – Simplify.
Do in notebook!
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Find the slope of the line that passes through (4, 1) and (-4, 1).
1. 02. 83. - 84. -1/8
Do in Notebook!
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Find the slope of the line that passes through (4, 1) and (-6, -4).
1. 22. -23. -1/24. 1/2
Do in Notebook!
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Find the slope of the line that passes through (-2, 4) and (10, 0).
1. 1/32. -1/33. -1/24. 1/2
Do in Notebook!
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Find the slope of the line that passes through (3, 2) and (3, -2).
1. 02. 43. -44. undefined
Do in Notebook!
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Find the slope of the line that passes through (2, 7) and (-2, -3).
1. 5/22. -5/23. -44. 0
Do in Notebook!
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Record notes in foldable first under Ordered Pairs heading.
Activity– Pass out worksheet. Find the slopes of the graphs.
Go ahead on slides for finding slopes other ways.
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Finding the slope of a line from a table
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Calculate slope from a table.X Y
1 10
2 20
3 30
4 40
5 50
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Is this function linear?Calculate slope from a table.
X Y
3 22
10 36
17 50
24 64
31 78
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Finding the slope from word
problems
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Slope from Word Problems
• The pitch of a roof is the number of feet the roof rises for each 12 feet horizontally. If a roof has a pitch of 8, what is the slope expressed as a positive number?
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Slope from Word Problems
• A daily newspaper had 12,125 subscribers when it began publication. Five years later it had 10,100 subscribers. What is the average yearly rate of change in the number of subscribers for the five year period?
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Drawing a line when given one point and the
slope
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1
Draw a line through the point (2,0) that has a slope of 3.
1. Graph the ordered pair (2, 0).2. From (2, 0), apply rise over
run (write 3 as a fraction).3. Plot a point at this location.4. Draw a straight line through
the points.
3
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If you know the slope and one point on the line you can draw the line.
Example: slope is 1/3 and the point (-2,-1)
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Now you draw a line.
• Given: slope is 2/3 and the point is (1,0)
• Given: slope is –3 and the point is (–2,4)
• Given: slope is 1 and the point is (2,3)
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Finding a missing
coordinate.
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The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r.
To solve this, plug the given information into the formula
m
( y2 y1)(x2 x1)
.
2 644 r
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4 41 4 r
To solve for r, simplify and write as a proportion.
4 41 4 r
2 644 r
Cross multiply.
1(-4) = 4(4 – r)
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Simplify and solve the equation.1(-4) = 4(4 – r)
-4 = 16 – 4r-16 -16-20 = -4r-4 -45 = r
The ordered pairs are (5, 6) and (4, 2)