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!

My dad left to get milk. He never came back :)

My mom gets milk every week, and she always comes back! I confuse.

Genuine question- when will i EVER use this IRL?

no but you will for your math class so

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.

So it doesn't matter then, what numbers you use for slope. What about when they don't give you a graph and make you find slope? I'm confused

You haven't said what information you were given instead of a graph. If you are given two points on the line, you can calculate the slope using the slope formula. If you are given the equation of the line, you can: -- Change the equation into slope-intercept form: y=mx+b and "m" will be the slope. -- Or, you can calculate two points using the equation and then use the slope formula to calculate the slope. All these options are covered in later videos.

Think of slope of a given graphed line in this way, and this is also very helpful when you want to calculate slope from a table or a formula. Slope = y2-y1/x2-x1 for any two points, 1 and 2, on the line or in the table, or calculated in the formula. In the opening graph of this page, the two points with the dots (though you could use any two points on the line) are (in standard x,y sequence): Point 1:(3,2) Point 2:(5,8) From those points, we get: y2-y1 = 8-2 = 6. x2-x1 = 5-3 = 2. Slope is now determined by y2-y1/x2-x1, or 6/2, or 3. I could also do y1-y2/x1-x2 instead of y2-y1/x2-x1, reversing the order of the points in the calculation and, sometimes, that's helpful to keep the algebra simple and positive. But, once calculated through, both ways yield the same results. For instance, in the case I am talking about, if we reverse the order of the points in our math, we get: y1-y2/x1-x2 = 2-8/3-5 or -6/-2. A negative divided by a negative yields a positive so -6/-2 = positive 3. That's the same result so I've proven the order of the two points in our calculation doesn't matter; it only requires that we keep the x and y order consistent throughout the calculations.

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 :)

Main content

Intro to slope

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 2 years 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...”
  (11 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 8 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)
28carpenters
Posted 4 months 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...”
(10 votes)
Answer
- alexanderkirilov4
  Posted 4 months 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
  (16 votes)
Mia
Posted a year ago. Direct link to Mia's post “My dad left to get milk. ...”
My dad left to get milk. He never came back :)
Button navigates to signup pageComment on Mia's post “My dad left to get milk. ...”
(16 votes)
Answer
- 🥤SomeSoda🥤
  Posted 5 months 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
  (2 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 6 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...”
  (23 votes)
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
Button navigates to signup pageComment on jonny.savois's post “lmao what is y=mx+b gonna...”
(9 votes)
Answer
sunyoung kim
Posted 3 months ago. Direct link to sunyoung kim's post “I ain’t understand”
I ain’t understand
Button navigates to signup pageButton navigates to signup page
(5 votes)
Answer
- dalepres
  Posted 3 months ago. Direct link to dalepres's post “Think of slope of a given...”
  Think of slope of a given graphed line in this way, and this is also very helpful when you want to calculate slope from a table or a formula.
  
  Slope = y2-y1/x2-x1 for any two points, 1 and 2, on the line or in the table, or calculated in the formula.
  
  In the opening graph of this page, the two points with the dots (though you could use any two points on the line) are (in standard x,y sequence):
  
  Point 1:(3,2)
  Point 2:(5,8)
  
  From those points, we get:
  
  y2-y1 = 8-2 = 6.
  x2-x1 = 5-3 = 2.
  
  Slope is now determined by y2-y1/x2-x1, or 6/2, or 3.
  
  I could also do y1-y2/x1-x2 instead of y2-y1/x2-x1, reversing the order of the points in the calculation and, sometimes, that's helpful to keep the algebra simple and positive. But, once calculated through, both ways yield the same results.
  
  For instance, in the case I am talking about, if we reverse the order of the points in our math, we get:
  
  y1-y2/x1-x2 = 2-8/3-5 or -6/-2.
  
  A negative divided by a negative yields a positive so -6/-2 = positive 3.
  
  That's the same result so I've proven the order of the two points in our calculation doesn't matter; it only requires that we keep the x and y order consistent throughout the calculations.
  Comment on dalepres's post “Think of slope of a given...”
  (7 votes)
kairly635
Posted a month ago. Direct link to kairly635's post “ma’am I do not get this🧍...”
ma’am I do not get this🧍🏻‍♀️
Button navigates to signup pageComment on kairly635's post “ma’am I do not get this🧍...”
(8 votes)
Answer
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)
PandaGirl
Posted 2 months ago. Direct link to PandaGirl's post “So it doesn't matter then...”
So it doesn't matter then, what numbers you use for slope. What about when they don't give you a graph and make you find slope? I'm confused
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- Kim Seidel
  Posted 2 months ago. Direct link to Kim Seidel's post “You haven't said what inf...”
  You haven't said what information you were given instead of a graph.
  
  If you are given two points on the line, you can calculate the slope using the slope formula.
  
  If you are given the equation of the line, you can:
  -- Change the equation into slope-intercept form: y=mx+b and "m" will be the slope.
  -- Or, you can calculate two points using the equation and then use the slope formula to calculate the slope.
  
  All these options are covered in later videos.
  Button navigates to signup page
  (4 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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