Finding Slope Rise over Run for elementary students

Jan 20, 2025Download as PPT, PDF0 likes13 views

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Intro to Slope rise over run

Objective
The student will be able to:
find the slope of a line given 2 points and
a graph.
SOL: A.6a
Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS

What is the meaning of this sign?
1. Icy Road Ahead
2. Steep Road Ahead
3. Curvy Road Ahead
4. 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%
So, what is slope???
Slope is the steepness of a line.
7 feet
100 feet

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 is
going downhill from left to right.
2 1
2 1
( ) vertical change
( ) horizontal change
y y rise
m
x x run

  


When given the graph, it is easier to apply
“rise over run”.
1) 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!
Determine the slope of the line.
6
3
run
3
6
= =
1
2
rise
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).
(1 ( 2))
(4 ( 2))
m
 

 
2 1
2 1
( )
( )
y y
m
x x



(1 2)
(4 2)



When given points, it is easier to use the formula!
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
3
6 2
 

Did you notice that Example #1 and
Example #2 were the same problem
written differently?
(-2, -2) and (4, 1)
6
3
1
2
slope 
You can do the problems either way!
Which one do you think is easiest?

Find the slope of the line that passes
through (3, 5) and (-1, 4).
1. 4
2. -4
3. ¼
4. - ¼

3) Find the slope of the line that goes
through the points (-5, 3) and (2, 1).
m 
y2  y1
x2  x1
1 3
2 ( 5)
m


 
1 3
2 5
m



2
7
m



Determine the slope of the line shown.
1. -2
2. -½
3. ½
4. 2

Determine the slope of the line.
The line is decreasing (slope is negative).
2
-1
rise
run

2
 1
 2
Find points on the graph.
Use two of them and
apply rise over run.

What is the slope of a horizontal line?
The line doesn’t rise!
m 
0
number
0
All horizontal lines have a slope of 0.

What is the slope of a vertical line?
The line doesn’t run!
All vertical lines have an undefined slope.
m 
number
0
undefined

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.

$1 Draw a line through the point (2,0) that has a slope of 3. 1. Graph the ordered pair (2, 0). 2. From (2, 0), apply rise over run (write 3 as a fraction). 3. Plot a point at this location. 4. Draw a straight line through the points. 3$

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 6
4
4 r




4 4
1 4 r



To solve for r, simplify and write as
a proportion.
4 4
1 4 r



2 6
4
4 r



Cross multiply.
1(-4) = 4(4 – r)

Simplify and solve the equation.
1(-4) = 4(4 – r)
-4 = 16 – 4r
-16 -16
-20 = -4r
-4 -4
5 = r
The ordered pairs are (5, 6) and (4, 2)

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Finding Slope Rise over Run for elementary students

1. Objective The student will be able to: find the slope of a line given 2 points and a graph. SOL: A.6a Designed by Skip Tyler, Varina HS and Vicki Hiner, Godwin HS

2. What is the meaning of this sign? 1. Icy Road Ahead 2. Steep Road Ahead 3. Curvy Road Ahead 4. Trucks Entering Highway Ahead

3. 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

4. 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 is going downhill from left to right. 2 1 2 1 ( ) vertical change ( ) horizontal change y y rise m x x run     

5. When given the graph, it is easier to apply “rise over run”. 1) Determine the slope of the line.

6. 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 run 3 6 = = 1 2 rise Notice the slope is positive AND the line increases!

7. 2) 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 y m x x    (1 2) (4 2)    When given points, it is easier to use the formula! 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 3 6 2  

8. Did you notice that Example #1 and Example #2 were the same problem written differently? (-2, -2) and (4, 1) 6 3 1 2 slope  You can do the problems either way! Which one do you think is easiest?

9. Find the slope of the line that passes through (3, 5) and (-1, 4). 1. 4 2. -4 3. ¼ 4. - ¼

10. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1). m  y2  y1 x2  x1 1 3 2 ( 5) m     1 3 2 5 m    2 7 m  

11. Determine the slope of the line shown. 1. -2 2. -½ 3. ½ 4. 2

12. Determine the slope of the line. The line is decreasing (slope is negative). 2 -1 rise run  2  1  2 Find points on the graph. Use two of them and apply rise over run.

13. What is the slope of a horizontal line? The line doesn’t rise! m  0 number 0 All horizontal lines have a slope of 0.

14. What is the slope of a vertical line? The line doesn’t run! All vertical lines have an undefined slope. m  number 0 undefined

15. 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.

16. 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

17. 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 6 4 4 r   

18. 4 4 1 4 r    To solve for r, simplify and write as a proportion. 4 4 1 4 r    2 6 4 4 r    Cross multiply. 1(-4) = 4(4 – r)

19. Simplify and solve the equation. 1(-4) = 4(4 – r) -4 = 16 – 4r -16 -16 -20 = -4r -4 -4 5 = r The ordered pairs are (5, 6) and (4, 2)

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Finding Slope Rise over Run for elementary students

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Finding Slope Rise over Run for elementary students