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Intro to slope

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

(3, 2)

and

(5, 8)

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

(3, 2)

and

(5, 8)

$Slope = \frac{Change in y}{Change in x} = \frac{6}{2} = 3$ ?

Use the graph below to find the slope of the line that goes through the points $(1, 2)$ ? and $(6, 6)$ ?.

Slope =

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

(2, 7)

and

(5, 1)

$Slope = \frac{Change in y}{Change in x} = \frac{? 6}{3} = ? 2$ ?

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 $(1, 9)$ ? and $(4, 0)$ ?.

Slope =

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

$Slope = \frac{Change in y}{Change in x} = \frac{Rise}{Run}$ ?

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 $(7, 4)$ ? and $(3, 2)$ ?.

Slope =

2) Use the graph below to find the slope of the line that goes through the points $(? 6, 9)$ ? and $(2, 1)$ ?.

Slope =

3) Use the graph below to find the slope of the line that goes through the points $(? 8, ? 3)$ ? and $(4, ? 6)$ ?.

Slope =

4) Use the graph below to find the slope of the line that goes through the points $(4, 5)$ ? and $(9, 5)$ ?.

Slope =

5) Use the graph below to choose the slope of the line that goes through the points $(3, 2)$ ? and $(3, 8)$ ?.

Slope =

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 $\frac{1}{2}$ ?

7) A line with a slope of $? 5$ ? is steeper than a line with a slope of $? \frac{1}{2}$ ?

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Tama Haydock
Posted 4 years ago. Direct link to Tama Haydock's post “why does math have to be ...”
why does math have to be so confusing?
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- Maya
  Posted a year 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!
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Mia
Posted 2 years 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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- ?SomeSoda?
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  My mom gets milk every week, and she always comes back! I confuse.
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Charlie Chan
Posted 8 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!
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(38 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...”
  (19 votes)
28carpenters
Posted a year ago. Direct link to 28carpenters's post “Genuine question- when wi...”
Genuine question- when will i EVER use this IRL?
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(20 votes)
Answer
- alexanderkirilov4
  Posted a year ago. Direct link to alexanderkirilov4's post “no but you will for your ...”
  no but you will for your math class so
  Comment on alexanderkirilov4's post “no but you will for your ...”
  (21 votes)
hyenzmacababbad
Posted 7 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?
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(9 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...”
  (36 votes)
kairly635
Posted 9 months ago. Direct link to kairly635's post “ma’am I do not get this?...”
ma’am I do not get this???♀?
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- landon.hon
  Posted 3 months ago. Direct link to landon.hon's post “who are you talking to”
  who are you talking to
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jonny.savois
Posted 5 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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(18 votes)
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- landon.hon
  Posted 3 months ago. Direct link to landon.hon's post “basically unless you plan...”
  basically unless you plan to be a nerd you wont need it
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Jake11
Posted 10 months ago. Direct link to Jake11'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
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(8 votes)
Answer
- Kim Seidel
  Posted 10 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.
  Comment on Kim Seidel's post “You haven't said what inf...”
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357961
Posted 8 months ago. Direct link to 357961's post “how does this affect me”
how does this affect me
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Answer
- R2Rem
  Posted 4 months ago. Direct link to R2Rem's post “You can use it to program...”
  You can use it to program. And to calculate landslides the steepness of hills or the angle of a roof.
  Comment on R2Rem's post “You can use it to program...”
  (1 vote)
Naomi-Ife Lagbara
Posted 7 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?
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(4 votes)
Answer
- Dominic Nguyen
  Posted 7 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...”
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8th grade

Course: 8th grade?>?Unit 3

Negative slope

Slope as "rise over run"

Let's practice!

Challenge problems

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