If the slope is 0, is a horizontal line. It makes sense if you think about it. Each time we increase one x, increase y by 0.

how do you find the slope and intercept on a graph?

To find the y-intercept, find where the line hits the y-axis. To find the x-intercept (which wasn't mentioned in the text), find where the line hits the x-axis. To find the slope, find two points on the line then do y2-y1/x2-x1 _the numbers are subscripts_. Hope that helped.

how does an equation result to an answer?

The equation results in how to graph the line on a graph. If they give you the x value then you would plug that in and it would tell you the answer in y.

I dont understand this whole thing at all PLEASE HELP!

The slope-intercept form of a linear equation is where one side contains just "y". So, it will look like: y = mx + b where "m" and "b" are numbers. This form of the equation is very useful. The coefficient of "x" (the "m" value) is the slope of the line. And, the constant (the "b" value) is the y-intercept at (0, b) So, if you are given an equation like: y = 2/3 (x) -5 We can tell that the slope of the line = 2/3 and the y-intercept is at (0, -5) Hope this helps.

Why should I learn this and what can I use this for in the future.

slopes are all over the place in the real world, so it depends on what you plan to do in life of how much you use this. Art, building, science, engineering, finance, statistics, etc. all use linear functions.

Is it ever possible that the slope of a linear function can fluctuate? Or is the slope always a fixed value?

It is a fixed value, but it could possibly look different. So if the slope is 2, you might find points that create a slope of 4/2 or 6/3 or 8/4 or maybe even 1/.5, but each of these will reduce to the same slope of 2.

Why is it called algebra? Is it Greek or something?

There is an overview history video in Algebra 1 that explains this better than I can but basically Algebra is a Medieval Latin short hand for the title of the first book explaining these principals. It was called "al-mukhtasar fi hisab al-jabr wa al-muqabala", which is Arabic for "the compendium on calculation by restoring and balancing". Here's the link to the vid if you want to explore further: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:algebra-overview-history/v/origins-of-algebra Hope I answered your question well! Best of luck learning🍀

say you have a problem like (3,1) slope= 4/3. how would you work that out

Pretty late here, but for anyone else reading, I'll assume they meant how you find the slope intercept using only these values. Since we know the slope is 4/3, we can conclude that: y = 4/3 * x ... But what is the constant, the y axis intercept point? You can solve for it by doing: 1 = 4/3 * 3 + c... We know the values for x and y at some point in the line, but we want to know the constant, c. You can solve this algebraically. 1 = 4/3 * 3 + c 1 = 4 + c 1 - 4 = 4 - 4 + c -3 = c The slope intercept equation is: y = 4/3 * x - 3 The y axis intercept point is: (0 , -3) I just started learning this so if anyone happens across this and spots an error lemme know.

How do I find the x intercept?

You use y=0 in the equation and calculate "x"

Just curious: how do derivatives differ from slopes?

Derivatives are instantaneous slopes, the line that is tangent to a curve at a given point. Slopes are broader to cover any line, not just tangent lines.

Main content

Course: Grade 8 math (FL B.E.S.T.) > Unit 4

Lesson 5: Intro to slope-intercept form

Intro to slope-intercept form

Google Classroom

Learn about the slope-intercept form of two-variable linear equations, and how to interpret it to find the slope and y-intercept of their line.

What you should be familiar with before taking this lesson

You should know what two-variable linear equations are. Specifically, you should know that the graph of such equations is a line. If this is new to you, check out our intro to two-variable equations.
You should also be familiar with the following properties of linear equations: $y$ ‍-intercept and $x$ ‍-intercept and slope.

What you will learn in this lesson

What is the slope-intercept form of two-variable linear equations
How to find the slope and the $y$ ‍-intercept of a line from its slope-intercept equation
How to find the equation of a line given its slope and $y$ ‍-intercept

What is slope-intercept form?

Slope-intercept is a specific form of linear equations. It has the following general structure. Drum roll ...

y = m x + b

Here,

m

and

b

can be any two real numbers. For example, these are linear equations in slope-intercept form:

$y = 2 x + 1$ ‍
$y = - 3 x + 2.7$ ‍
$y = 10 - 100 x$ ‍

On the other hand, these linear equations are not in slope-intercept form:

$2 x + 3 y = 5$ ‍
$y - 3 = 2 (x - 1)$ ‍
$x = 4 y - 7$ ‍

Slope-intercept is the most prominent form of linear equations. Let's dig deeper to learn why this is so.

The coefficients in slope-intercept form

Besides being neat and simplified, slope-intercept form's advantage is that it gives two main features of the line it represents:

The slope is $m$ ‍.
The $y$ ‍-coordinate of the $y$ ‍-intercept is $b$ ‍. In other words, the line's $y$ ‍-intercept is at $(0, b)$ ‍.

For example, the line

y = 2 x + 1

has a slope of

2

and a

y

-intercept at

(0, 1)

The fact that this form gives the slope and the

y

-intercept is the reason why it is called slope-intercept in the first place!

Check your understanding

Problem 1

What is the slope of the line represented by $y = 5 x - 7$ ‍?

Problem 2

What is the slope of the line represented by $y = x + 9$ ‍?

Problem 3

What is the $y$ ‍-intercept of the line represented by $y = - 6 x - 11$ ‍?

Problem 4

What is the $y$ ‍-intercept of the line represented by $y = 4 x$ ‍?

Problem 5

What is the slope of the line represented by $y = 1 - 8 x$ ‍?

Problem 6

Which lines have a $y$ ‍-intercept at $(0, 4)$ ‍?

Reflection question

How do we find the slope of a line that is given in slope-intercept form?

Challenge problem 1

Which of these can be the equation of the line?

Challenge problem 2

Write an equation of a line whose slope is $10$ ‍ and $y$ ‍-intercept is $(0, - 20)$ ‍.

Why does this work?

You might be wondering how it is that in slope-intercept form,

m

gives the slope and

b

gives the

y

-intercept.

Can this be some sort of magic? Well, it certainly is not magic. In math, there's always a justification. In this section we'll take a look at this property using the equation

y = 2 x + 1

as an example.

Why $b$ ‍ gives the $y$ ‍-intercept

At the

y

-intercept, the

x

-value is always zero. So if we want to find the

y

-intercept of

y = 2 x + 1

, we should substitute

x = 0

and solve for

y

\begin{aligned} y & = 2 x + 1 \\ = 2 \cdot 0 + 1 & Substitute x = 0 \\ = 0 + 1 \\ = 1 \end{aligned}

We see that at the

y

-intercept,

2 x

becomes zero, and therefore we are left with

y = 1

Why $m$ ‍ gives the slope

Let's refresh our memories about what slope is exactly. Slope is the ratio of the change in

y

over the change in

x

between any two points on the line.

Slope = \frac{Change in y}{Change in x}

If we take two points where the change in

x

is exactly

1

unit, then the change in

y

will be equal to the slope itself.

Slope = \frac{Change in y}{1} = Change in y

Now let's look at what happens to the

y

-values in the equation

y = 2 x + 1

as the

x

-values constantly increase by

1

unit.

$x$ ‍	$y$ ‍
$0$ ‍	$1 + 0 \cdot 2$ ‍	$= 1$ ‍
$1$ ‍	$1 + 1 \cdot 2$ ‍	$= 1 + 2$ ‍
$2$ ‍	$1 + 2 \cdot 2$ ‍	$= 1 + 2 + 2$ ‍
$3$ ‍	$1 + 3 \cdot 2$ ‍	$= 1 + 2 + 2 + 2$ ‍
$4$ ‍	$1 + 4 \cdot 2$ ‍	$= 1 + 2 + 2 + 2 + 2$ ‍

We see that each time

x

increases by

1

unit,

y

increases by

2

units. This is because

x

determines the multiple of

2

in the calculation of

y

As stated above, the change in

y

that corresponds to

x

increasing by

1

unit is equal to the slope of the line. For this reason, the slope is

2

Let's look at what happens to the

y

-values in the general equation

y = m x + b

as the

x

-values constantly increase by

1

unit.

$x$ ‍	$y$ ‍
$0$ ‍	$b + 0 \cdot m$ ‍	$= b$ ‍
$1$ ‍	$b + 1 \cdot m$ ‍	$= b + m$ ‍
$2$ ‍	$b + 2 \cdot m$ ‍	$= b + m + m$ ‍
$3$ ‍	$b + 3 \cdot m$ ‍	$= b + m + m + m$ ‍
$4$ ‍	$b + 4 \cdot m$ ‍	$= b + m + m + m + m$ ‍

We see that each time

x

increases by

1

unit,

y

increases by

m

units. This is because

x

determines the multiple of

m

in the calculation of

y

As stated above, the change in

y

that corresponds to

x

increasing by

1

unit is equal to the slope of the line. For this reason,

m

always gives the slope.

Challenge problem 3

Complete the equation of the line.

y =

Want to join the conversation?

Sort by:

Patrice Abbee
Posted 6 years ago. Direct link to Patrice Abbee's post “What if m=0?”
What if m=0?
Button navigates to signup pageComment on Patrice Abbee's post “What if m=0?”
(53 votes)
Answer
- Admiral Betasin
  Posted 6 years ago. Direct link to Admiral Betasin's post “If the slope is 0, is a h...”
  If the slope is 0, is a horizontal line. It makes sense if you think about it. Each time we increase one x, increase y by 0.
  Comment on Admiral Betasin's post “If the slope is 0, is a h...”
  (149 votes)
faith reinhold
Posted 5 years ago. Direct link to faith reinhold's post “how do you find the slope...”
how do you find the slope and intercept on a graph?
Button navigates to signup pageComment on faith reinhold's post “how do you find the slope...”
(28 votes)
Answer
- Karra Wallis
  Posted 4 years ago. Direct link to Karra Wallis's post “To find the y-intercept, ...”
  To find the y-intercept, find where the line hits the y-axis. To find the x-intercept (which wasn't mentioned in the text), find where the line hits the x-axis. To find the slope, find two points on the line then do y2-y1/x2-x1 the numbers are subscripts.
  Hope that helped.
  Comment on Karra Wallis's post “To find the y-intercept, ...”
  (38 votes)
Varahi
Posted 7 years ago. Direct link to Varahi's post “I dont understand this wh...”
I dont understand this whole thing at all PLEASE HELP!
Button navigates to signup pageComment on Varahi's post “I dont understand this wh...”
(21 votes)
Answer
- Kim Seidel
  Posted 7 years ago. Direct link to Kim Seidel's post “The slope-intercept form ...”
  The slope-intercept form of a linear equation is where one side contains just "y". So, it will look like: y = mx + b where "m" and "b" are numbers.
  This form of the equation is very useful. The coefficient of "x" (the "m" value) is the slope of the line. And, the constant (the "b" value) is the y-intercept at (0, b)
  So, if you are given an equation like: y = 2/3 (x) -5
  We can tell that the slope of the line = 2/3 and the y-intercept is at (0, -5)
  Hope this helps.
  Comment on Kim Seidel's post “The slope-intercept form ...”
  (33 votes)
Carson Payne
Posted 7 years ago. Direct link to Carson Payne's post “how does an equation resu...”
how does an equation result to an answer?
Button navigates to signup pageComment on Carson Payne's post “how does an equation resu...”
(23 votes)
Answer
- hancockandrewj
  Posted 3 years ago. Direct link to hancockandrewj's post “The equation results in h...”
  The equation results in how to graph the line on a graph. If they give you the x value then you would plug that in and it would tell you the answer in y.
  Comment on hancockandrewj's post “The equation results in h...”
  (9 votes)
Henry Mays
Posted a year ago. Direct link to Henry Mays's post “Why should I learn this a...”
Why should I learn this and what can I use this for in the future.
Button navigates to signup pageComment on Henry Mays's post “Why should I learn this a...”
(13 votes)
Answer
- David Severin
  Posted a year ago. Direct link to David Severin's post “slopes are all over the p...”
  slopes are all over the place in the real world, so it depends on what you plan to do in life of how much you use this. Art, building, science, engineering, finance, statistics, etc. all use linear functions.
  Comment on David Severin's post “slopes are all over the p...”
  (14 votes)
deepasaji
Posted 9 months ago. Direct link to deepasaji's post “Why is it called algebra?...”
Why is it called algebra? Is it Greek or something?
Button navigates to signup pageComment on deepasaji's post “Why is it called algebra?...”
(5 votes)
Answer
- Rose🌹
  Posted 9 months ago. Direct link to Rose🌹's post “There is an overview hist...”
  There is an overview history video in Algebra 1 that explains this better than I can but basically Algebra is a Medieval Latin short hand for the title of the first book explaining these principals.
  It was called "al-mukhtasar fi hisab al-jabr wa al-muqabala", which is Arabic for "the compendium on calculation by restoring and balancing".
  Here's the link to the vid if you want to explore further: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:foundation-algebra/x2f8bb11595b61c86:algebra-overview-history/v/origins-of-algebra
  Hope I answered your question well! Best of luck learning🍀
  Comment on Rose🌹's post “There is an overview hist...”
  (22 votes)
Vector Inc.
Posted 4 years ago. Direct link to Vector Inc.'s post “Is it ever possible that ...”
Is it ever possible that the slope of a linear function can fluctuate? Or is the slope always a fixed value?
Button navigates to signup pageButton navigates to signup page
(10 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “It is a fixed value, but ...”
  It is a fixed value, but it could possibly look different. So if the slope is 2, you might find points that create a slope of 4/2 or 6/3 or 8/4 or maybe even 1/.5, but each of these will reduce to the same slope of 2.
  Comment on David Severin's post “It is a fixed value, but ...”
  (6 votes)
kendellnoble2002
Posted 7 years ago. Direct link to kendellnoble2002's post “say you have a problem li...”
say you have a problem like (3,1) slope= 4/3. how would you work that out
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Rei
  Posted 4 years ago. Direct link to Rei's post “Pretty late here, but for...”
  Pretty late here, but for anyone else reading, I'll assume they meant how you find the slope intercept using only these values.
  
  Since we know the slope is 4/3, we can conclude that: y = 4/3 * x ... But what is the constant, the y axis intercept point?
  
  You can solve for it by doing: 1 = 4/3 * 3 + c... We know the values for x and y at some point in the line, but we want to know the constant, c. You can solve this algebraically.
  1 = 4/3 * 3 + c
  1 = 4 + c
  1 - 4 = 4 - 4 + c
  -3 = c
  
  The slope intercept equation is: y = 4/3 * x - 3
  
  The y axis intercept point is: (0 , -3)
  
  I just started learning this so if anyone happens across this and spots an error lemme know.
  Comment on Rei's post “Pretty late here, but for...”
  (8 votes)
Alex
Posted a year ago. Direct link to Alex's post “How do I find the x inter...”
How do I find the x intercept?
Button navigates to signup pageComment on Alex's post “How do I find the x inter...”
(3 votes)
Answer
- Kim Seidel
  Posted a year ago. Direct link to Kim Seidel's post “You use y=0 in the equati...”
  You use y=0 in the equation and calculate "x"
  Button navigates to signup page
  (8 votes)
Gabyscience
Posted 10 months ago. Direct link to Gabyscience's post “Just curious: how do deri...”
Just curious: how do derivatives differ from slopes?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- David Severin
  Posted 9 months ago. Direct link to David Severin's post “Derivatives are instantan...”
  Derivatives are instantaneous slopes, the line that is tangent to a curve at a given point. Slopes are broader to cover any line, not just tangent lines.
  Button navigates to signup page
  (10 votes)

Grade 8 math (FL B.E.S.T.)

Course: Grade 8 math (FL B.E.S.T.) > Unit 4

What you should be familiar with before taking this lesson

What you will learn in this lesson

What is slope-intercept form?

The coefficients in slope-intercept form

Check your understanding

Why does this work?

Why b‍ gives the y‍ -intercept

Why m‍ gives the slope

Want to join the conversation?

Why $b$ ‍ gives the $y$ ‍-intercept

Why $m$ ‍ gives the slope