How can the slope value (1/2 or 5) be used in real life, and how can we use it in math? Thanks!

It could be used to simulate the steepness of a mountain/hill.

why does math have to be so confusing?

If you work hard then eventually math won't be as confusing!

Can somebody tell me how to easily visualized. which slope is steeper?

Try to think about it like this, imagine you are running up (positive slope) or down (negative slope) a flight of stairs. If the slope is a larger number, than it is the same as taking several steps at once. If the slope is a smaller number, it is as if you are taking less steps at once, not going up the flight of stairs as quickly. Imagine a slope of 1, means for ever step you take with your feet you only go up one stair. Imagine a slope of 5, this means for every step you take you go up 5 stairs. You get to the top and rise much quicker. _____________ Another visual example: Imagine you are going skiing. As you go down a slope, you expect the slope to be negative. You come from up high on the y axis and go down. If now you go to a ski slope at -5 that means for every meter you glide forward on your skis towards to bottom of the hill (x-axis), you also go down 5 meters on the hills height (y-axis). This is very steep as you can imagine. Now imagine you are going down a ski slope of only 1/2. This means for every 1 meter you glide forward on your ski you only get 1/2 meter further down the hills height.

Genuine question- when will i EVER use this IRL?

no but you will for your math class so

Is there another way of finding a slope without a graph?

It should give you points on the graph, use the formula y2-y1/x2-x1, to find the slope, (y2 a y-coordinate, of one of the point, you are not multiplying anything) Hope this helps :)

What does steeper mean, greater slope? In that case, shouldn't a slope of -1/2 be steeper than -5, as -1/2 is greater than -5?

We are seeing _absolute value_, which means if it's negative, we have to see the *more negative* one as the greater one. If it's positive, we have to see the more positive one as the greater one(like we always did) The symbol for absolute values are like so: | _insert number_ | Try these problems as examples: Put > < = in the blanks. a) | -6 | __ | -1 | b) | 8 | __ | 9 | c) | -4 | __ | -12 | The answers are a) > b) < c) <

is there an easier way to find the slope?

yes, actually if you align the coordinates For example: (3,2) (5,8) And then you would find the difference between the the numbers such as the difference between the 3 and 5 is 2, while the difference in the 2 and 8 is 6. After you get these numbers you can put them in the fraction form as you would after you find the numbers on the graph.This would then equal 6/2 or in simplified form = 3. I hope this was helpful (:

Main content

Intro to slope

Q: is there an easier way to find the slope?

yes, actually if you align the coordinates For example: (3,2) (5,8) And then you would find the difference between the the numbers such as the difference between the 3 and 5 is 2, while the difference in the 2 and 8 is 6. After you get these numbers you can put them in the fraction form as you would after you find the numbers on the graph.This would then equal 6/2 or in simplified form = 3. I hope this was helpful (:

CCSS.Math:

8.F.B.4

Google Classroom

Walk through a graphical explanation of how to find the slope from two points and what it means.

We can draw a line through any two points on the coordinate plane.

Let's take the points left parenthesis, 3, comma, 2, right parenthesis and left parenthesis, 5, comma, 8, right parenthesis as an example:

The slope of a line describes how steep a line is. Slope is the change in y values divided by the change in x values.

Let's find the slope of the line that goes through the points left parenthesis, 3, comma, 2, right parenthesis and left parenthesis, 5, comma, 8, right parenthesis:

start text, S, l, o, p, e, end text, equals, start fraction, start color #e07d10, start text, C, h, a, n, g, e, space, i, n, space, y, end text, end color #e07d10, divided by, start color #1fab54, start text, C, h, a, n, g, e, space, i, n, space, x, end text, end color #1fab54, end fraction, equals, start fraction, start color #e07d10, 6, end color #e07d10, divided by, start color #1fab54, 2, end color #1fab54, end fraction, equals, 3

Use the graph below to find the slope of the line that goes through the points left parenthesis, 1, comma, 2, right parenthesis and left parenthesis, 6, comma, 6, right parenthesis.

start text, S, l, o, p, e, end text, equals

[Show solution]

Notice that both of the lines we've looked at so far have been increasing and have had positive slopes as a result. Now let's find the slope of a decreasing line.

Negative slope

Let's find the slope of the line that goes through the points left parenthesis, 2, comma, 7, right parenthesis and left parenthesis, 5, comma, 1, right parenthesis.

start text, S, l, o, p, e, end text, equals, start fraction, start color #e07d10, start text, C, h, a, n, g, e, space, i, n, space, y, end text, end color #e07d10, divided by, start color #1fab54, start text, C, h, a, n, g, e, space, i, n, space, x, end text, end color #1fab54, end fraction, equals, start fraction, start color #e07d10, minus, 6, end color #e07d10, divided by, start color #1fab54, 3, end color #1fab54, end fraction, equals, minus, 2

Wait a minute! Did you catch that? The change in y values is negative because we went from 7 down to 1. This led to a negative slope, which makes sense because the line is decreasing.

Use the graph below to find the slope of the line that goes through the points left parenthesis, 1, comma, 9, right parenthesis and left parenthesis, 4, comma, 0, right parenthesis.

start text, S, l, o, p, e, end text, equals

[Show solution]

Slope as "rise over run"

A lot of people remember slope as "rise over run" because slope is the "rise" (change in y) divided by the "run" (change in x).

start text, S, l, o, p, e, end text, equals, start fraction, start color #e07d10, start text, C, h, a, n, g, e, space, i, n, space, y, end text, end color #e07d10, divided by, start color #1fab54, start text, C, h, a, n, g, e, space, i, n, space, x, end text, end color #1fab54, end fraction, equals, start fraction, start color #e07d10, start text, R, i, s, e, end text, end color #e07d10, divided by, start color #1fab54, start text, R, u, n, end text, end color #1fab54, end fraction

Let's practice!

Heads up! All of the examples we've seen so far have been points in the first quadrant, but that won't always be the case in the practice problems.

1) Use the graph below to find the slope of the line that goes through the points left parenthesis, 7, comma, 4, right parenthesis and left parenthesis, 3, comma, 2, right parenthesis.

start text, S, l, o, p, e, end text, equals

[Show solution]

2) Use the graph below to find the slope of the line that goes through the points left parenthesis, minus, 6, comma, 9, right parenthesis and left parenthesis, 2, comma, 1, right parenthesis.

start text, S, l, o, p, e, end text, equals

[Show solution]

3) Use the graph below to find the slope of the line that goes through the points left parenthesis, minus, 8, comma, minus, 3, right parenthesis and left parenthesis, 4, comma, minus, 6, right parenthesis.

start text, S, l, o, p, e, end text, equals

[Show solution]

4) Use the graph below to find the slope of the line that goes through the points left parenthesis, 4, comma, 5, right parenthesis and left parenthesis, 9, comma, 5, right parenthesis.

start text, S, l, o, p, e, end text, equals

[Show solution]

5) Use the graph below to choose the slope of the line that goes through the points left parenthesis, 3, comma, 2, right parenthesis and left parenthesis, 3, comma, 8, right parenthesis.

start text, S, l, o, p, e, end text, equals

[Show solution]

Challenge problems

See how well you understand slope by trying a couple of true/false problems.

6) A line with a slope of 5 is steeper than a line with a slope of start fraction, 1, divided by, 2, end fraction

[Show solution]

7) A line with a slope of minus, 5 is steeper than a line with a slope of minus, start fraction, 1, divided by, 2, end fraction

[Show solution]

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Charlie Chan
Posted 7 years ago. Direct link to Charlie Chan's post “How can the slope value (...”
How can the slope value (1/2 or 5) be used in real life, and how can we use it in math?

Thanks!
Button navigates to signup pageComment on Charlie Chan's post “How can the slope value (...”
(33 votes)
Answer
- BlahBlahBlah Studios
  Posted a year ago. Direct link to BlahBlahBlah Studios's post “It could be used to simul...”
  It could be used to simulate the steepness of a mountain/hill.
  Comment on BlahBlahBlah Studios's post “It could be used to simul...”
  (9 votes)
Tama Haydock
Posted 3 years ago. Direct link to Tama Haydock's post “why does math have to be ...”
why does math have to be so confusing?
Button navigates to signup pageComment on Tama Haydock's post “why does math have to be ...”
(30 votes)
Answer
- Maya
  Posted 4 months ago. Direct link to Maya's post “If you work hard then eve...”
  If you work hard then eventually math won't be as confusing!
  Comment on Maya's post “If you work hard then eve...”
  (9 votes)
hyenzmacababbad
Posted 6 years ago. Direct link to hyenzmacababbad's post “Can somebody tell me how ...”
Can somebody tell me how to easily visualized. which slope is steeper?
Button navigates to signup pageComment on hyenzmacababbad's post “Can somebody tell me how ...”
(6 votes)
Answer
- Ina
  Posted 5 years ago. Direct link to Ina's post “Try to think about it lik...”
  Try to think about it like this, imagine you are running up (positive slope) or down (negative slope) a flight of stairs.
  
  If the slope is a larger number, than it is the same as taking several steps at once.
  If the slope is a smaller number, it is as if you are taking less steps at once, not going up the flight of stairs as quickly.
  
  Imagine a slope of 1, means for ever step you take with your feet you only go up one stair.
  
  Imagine a slope of 5, this means for every step you take you go up 5 stairs. You get to the top and rise much quicker.
  
  ___________
  
  Another visual example: Imagine you are going skiing. As you go down a slope, you expect the slope to be negative. You come from up high on the y axis and go down.
  
  If now you go to a ski slope at -5 that means for every meter you glide forward on your skis towards to bottom of the hill (x-axis), you also go down 5 meters on the hills height (y-axis). This is very steep as you can imagine.
  
  Now imagine you are going down a ski slope of only 1/2. This means for every 1 meter you glide forward on your ski you only get 1/2 meter further down the hills height.
  Comment on Ina's post “Try to think about it lik...”
  (24 votes)
Mia
Posted 7 months ago. Direct link to Mia's post “My dad left to get milk. ...”
My dad left to get milk. He never came back :)
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(16 votes)
Answer
- 🥤SomeSoda🥤
  Posted a month ago. Direct link to 🥤SomeSoda🥤's post “My mom gets milk every we...”
  My mom gets milk every week, and she always comes back! I confuse.
  Button navigates to signup page
  (1 vote)
jonny.savois
Posted 4 years ago. Direct link to jonny.savois's post “lmao what is y=mx+b gonna...”
lmao what is y=mx+b gonna do for me in life
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(9 votes)
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Ingrid
Posted 7 years ago. Direct link to Ingrid's post “Wait, if it's based on ab...”
Wait, if it's based on absolute value, how come in the video Slope & direction of a line, it was that the lesser negative was greater?
Button navigates to signup pageButton navigates to signup page
(9 votes)
Answer
- Seed Something
  Posted a year ago. Direct link to Seed Something's post “In the Slope and Directio...”
  In the Slope and Direction video we were determining a slope's direction on the number line, its location, and using values of specific numbers, so we were using the number line, (and smaller negative numbers have a greater value, as they are closer to zero and positive values).
  
  But…
  ★for Steepness we're no longer comparing direction or location, we're now comparing how vertical a line is to another.
  
  By comparing the absolute values of the slopes we can find which line has a greater change in y than the relative change to x.
  
  Find which line increases or decreases further and faster on the y-axis than another line.
  
  So by finding which is furthest from zero, the one with the greater absolute value, we know which line is steeper and had a more extreme change in y than the other line.
  
  (ㆁωㆁ) Hope this helps someone!
  Comment on Seed Something's post “In the Slope and Directio...”
  (0 votes)
28carpenters
Posted 15 days ago. Direct link to 28carpenters's post “Genuine question- when wi...”
Genuine question- when will i EVER use this IRL?
Button navigates to signup pageComment on 28carpenters's post “Genuine question- when wi...”
(6 votes)
Answer
- alexanderkirilov4
  Posted 6 days ago. Direct link to alexanderkirilov4's post “no but you will for your ...”
  no but you will for your math class so
  Button navigates to signup page
  (4 votes)
Naomi-Ife Lagbara
Posted 6 years ago. Direct link to Naomi-Ife Lagbara's post “Is there another way of f...”
Is there another way of finding a slope without a graph?
Button navigates to signup pageComment on Naomi-Ife Lagbara's post “Is there another way of f...”
(3 votes)
Answer
- Dominic Nguyen
  Posted 6 years ago. Direct link to Dominic Nguyen's post “It should give you points...”
  It should give you points on the graph, use the formula y2-y1/x2-x1, to find the slope, (y2 a y-coordinate, of one of the point, you are not multiplying anything)
  Hope this helps :)
  Comment on Dominic Nguyen's post “It should give you points...”
  (10 votes)
Chinmay Joshi
Posted 7 years ago. Direct link to Chinmay Joshi's post “What does steeper mean, g...”
What does steeper mean, greater slope? In that case, shouldn't a slope of -1/2 be steeper than -5, as -1/2 is greater than -5?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Kayla Aurellia
  Posted 7 years ago. Direct link to Kayla Aurellia's post “We are seeing _absolute v...”
  We are seeing absolute value, which means if it's negative, we have to see the more negative one as the greater one. If it's positive, we have to see the more positive one as the greater one(like we always did)
  The symbol for absolute values are like so: | insert number |
  
  Try these problems as examples:
  Put > < = in the blanks.
  a) | -6 | _ | -1 |
  b) | 8 | _ | 9 |
  c) | -4 | __ | -12 |
  
  The answers are
  a) > b) < c) <
  Button navigates to signup page
  (9 votes)
yanet.sanchez1207
Posted 4 years ago. Direct link to yanet.sanchez1207's post “is there an easier way to...”
is there an easier way to find the slope?
Button navigates to signup pageComment on yanet.sanchez1207's post “is there an easier way to...”
(2 votes)
Answer
- Haleen
  Posted 4 years ago. Direct link to Haleen's post “yes, actually if you alig...”
  yes, actually if you align the coordinates
  For example: (3,2)
  (5,8)
  And then you would find the difference between the the numbers such as the difference between the 3 and 5 is 2, while the difference in the 2 and 8 is 6. After you get these numbers you can put them in the fraction form as you would after you find the numbers on the graph.This would then equal 6/2 or in simplified form = 3.
  I hope this was helpful (:
  Comment on Haleen's post “yes, actually if you alig...”
  (9 votes)

8th grade

Course: 8th grade > Unit 3

Intro to slope

Negative slope

Slope as "rise over run"

Let's practice!

Challenge problems

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