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.

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 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.

I am so lost I need help :((

The start of the lesson states what you should have some understanding of, so the first question is do you have some understanding of these two concepts? "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." If these are an issue, you need to go back and review these concepts. If you understand these, then you need to be more specific on where you are struggling. This is just an intro, so it is basically identifying slope and intercept from an equation. Which checks do not make sense?

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.

So here's my issue: I answered most of the questions on here correctly, but that was only because everything was repetitive and I kind of got the hang of it after a while. But I don't like using this method, because if I'm sitting say, in my SAT(I'm in 7th grade lol), I won't know if I answered the question about slope intercept form correctly because I won't have any examples explaining this to me! Does anyone have an easy, fool-proof way of remembering this and actually understanding it?! Thx sooo much.

Many processes in math take practice, practice and more practice. The more you practice, the less you need to have examples to look at.

What if the y-intercept is 0? What happens then?

Then the equation becomes: y=mx since "b" is 0, it is not shown.

Main content

Algebra 1

Course: Algebra 1 > Unit 5

Lesson 1: Intro to slope-intercept form

Intro to slope-intercept form

CCSS.Math:

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, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #0d923f, b, end color #0d923f

Here, start color #ed5fa6, m, end color #ed5fa6 and start color #0d923f, b, end color #0d923f can be any two real numbers. For example, these are linear equations in slope-intercept form:

y, equals, 2, x, plus, 1
y, equals, minus, 3, x, plus, 2, point, 7
y, equals, 10, minus, 100, x
[But this equation has x in the last term!]

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

2, x, plus, 3, y, equals, 5
y, minus, 3, equals, 2, left parenthesis, x, minus, 1, right parenthesis
x, equals, 4, y, minus, 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 start color #ed5fa6, m, end color #ed5fa6.
The y-coordinate of the y-intercept is start color #0d923f, b, end color #0d923f. In other words, the line's y-intercept is at left parenthesis, 0, comma, start color #0d923f, b, end color #0d923f, right parenthesis.

For example, the line y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, start color #0d923f, plus, 1, end color #0d923f has a slope of start color #ed5fa6, 2, end color #ed5fa6 and a y-intercept at left parenthesis, 0, comma, start color #0d923f, 1, end color #0d923f, right parenthesis:

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, equals, 5, x, minus, 7?

Problem 2

What is the slope of the line represented by y, equals, x, plus, 9?

Problem 3

What is the y-intercept of the line represented by y, equals, minus, 6, x, minus, 11?

(Choice A)
left parenthesis, 0, comma, minus, 6, right parenthesis
(Choice B)
left parenthesis, 0, comma, minus, 11, right parenthesis
(Choice C)
left parenthesis, minus, 6, comma, 0, right parenthesis
(Choice D)
left parenthesis, minus, 11, comma, 0, right parenthesis

Problem 4

What is the y-intercept of the line represented by y, equals, 4, x?

(Choice A)
left parenthesis, 0, comma, 0, right parenthesis
(Choice B)
left parenthesis, 0, comma, start fraction, 1, divided by, 4, end fraction, right parenthesis
(Choice C)
left parenthesis, 0, comma, 4, right parenthesis
(Choice D)
left parenthesis, 0, comma, minus, 4, right parenthesis

Problem 5

What is the slope of the line represented by y, equals, 1, minus, 8, x?

Problem 6

Which lines have a y-intercept at left parenthesis, 0, comma, 4, right parenthesis?

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 left parenthesis, 0, comma, minus, 20, right parenthesis.

Why does this work?

You might be wondering how it is that in slope-intercept form, start color #ed5fa6, m, end color #ed5fa6 gives the slope and start color #0d923f, b, end color #0d923f 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, equals, start color #ed5fa6, 2, end color #ed5fa6, x, plus, start color #0d923f, 1, end color #0d923f as an example.

Why start color #0d923f, b, end color #0d923f 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, equals, start color #ed5fa6, 2, end color #ed5fa6, x, plus, start color #0d923f, 1, end color #0d923f, we should substitute x, equals, 0 and solve for y.

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

We see that at the y-intercept, start color #ed5fa6, 2, end color #ed5fa6, x becomes zero, and therefore we are left with y, equals, start color #0d923f, 1, end color #0d923f.

[I want to see a proof using the general form y=mx+b!]

Why start color #ed5fa6, m, end color #ed5fa6 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.

start text, S, l, o, p, e, end text, equals, start fraction, start text, C, h, a, n, g, e, space, i, n, space, end text, y, divided by, start text, C, h, a, n, g, e, space, i, n, space, end text, x, end fraction

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.

start text, S, l, o, p, e, end text, equals, start fraction, start text, C, h, a, n, g, e, space, i, n, space, end text, y, divided by, 1, end fraction, equals, start text, C, h, a, n, g, e, space, i, n, space, end text, y

Now let's look at what happens to the y-values in the equation y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, plus, start color #0d923f, 1, end color #0d923f as the x-values constantly increase by 1 unit.

x	y
0	start color #0d923f, 1, end color #0d923f, plus, 0, dot, start color #ed5fa6, 2, end color #ed5fa6	equals, start color #0d923f, 1, end color #0d923f
1	start color #0d923f, 1, end color #0d923f, plus, 1, dot, start color #ed5fa6, 2, end color #ed5fa6	equals, start color #0d923f, 1, end color #0d923f, plus, start color #ed5fa6, 2, end color #ed5fa6
2	start color #0d923f, 1, end color #0d923f, plus, 2, dot, start color #ed5fa6, 2, end color #ed5fa6	equals, start color #0d923f, 1, end color #0d923f, plus, start color #ed5fa6, 2, end color #ed5fa6, plus, start color #ed5fa6, 2, end color #ed5fa6
3	start color #0d923f, 1, end color #0d923f, plus, 3, dot, start color #ed5fa6, 2, end color #ed5fa6	equals, start color #0d923f, 1, end color #0d923f, plus, start color #ed5fa6, 2, end color #ed5fa6, plus, start color #ed5fa6, 2, end color #ed5fa6, plus, start color #ed5fa6, 2, end color #ed5fa6
4	start color #0d923f, 1, end color #0d923f, plus, 4, dot, start color #ed5fa6, 2, end color #ed5fa6	equals, start color #0d923f, 1, end color #0d923f, plus, start color #ed5fa6, 2, end color #ed5fa6, plus, start color #ed5fa6, 2, end color #ed5fa6, plus, start color #ed5fa6, 2, end color #ed5fa6, plus, start color #ed5fa6, 2, end color #ed5fa6

We see that each time x increases by 1 unit, y increases by start color #ed5fa6, 2, end color #ed5fa6 units. This is because x determines the multiple of start color #ed5fa6, 2, end color #ed5fa6 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 start color #ed5fa6, 2, end color #ed5fa6.

[I want to see a proof using the general form y=mx+b!]

Challenge problem 3

Complete the equation of the line.

y, equals

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Patrice Abbee
Posted 5 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?”
(40 votes)
Answer
- Admiral Betasin
  Posted 5 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...”
  (98 votes)
faith reinhold
Posted 4 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...”
(27 votes)
Answer
- Karra Wallis
  Posted 3 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, ...”
  (33 votes)
Varahi
Posted 6 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...”
(16 votes)
Answer
- Kim Seidel
  Posted 6 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 ...”
  (20 votes)
Carson Payne
Posted 5 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...”
(20 votes)
Answer
- hancockandrewj
  Posted 2 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.
  Button navigates to signup page
  (7 votes)
Vector Inc.
Posted 3 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 3 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 ...”
  (4 votes)
Henry Mays
Posted 4 months 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 pageButton navigates to signup page
(7 votes)
Answer
- David Severin
  Posted 4 months 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...”
  (7 votes)
kendellnoble2002
Posted 6 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 3 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...”
  (7 votes)
Karina Rutann
Posted 10 months ago. Direct link to Karina Rutann's post “I am so lost I need help ...”
I am so lost I need help :((
Button navigates to signup pageComment on Karina Rutann's post “I am so lost I need help ...”
(5 votes)
Answer
- David Severin
  Posted 10 months ago. Direct link to David Severin's post “The start of the lesson s...”
  The start of the lesson states what you should have some understanding of, so the first question is do you have some understanding of these two concepts?
  "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."
  If these are an issue, you need to go back and review these concepts. If you understand these, then you need to be more specific on where you are struggling. This is just an intro, so it is basically identifying slope and intercept from an equation. Which checks do not make sense?
  Comment on David Severin's post “The start of the lesson s...”
  (2 votes)
Saule 🍄✨💜
Posted 3 years ago. Direct link to Saule 🍄✨💜's post “So here's my issue: I ans...”
So here's my issue: I answered most of the questions on here correctly, but that was only because everything was repetitive and I kind of got the hang of it after a while. But I don't like using this method, because if I'm sitting say, in my SAT(I'm in 7th grade lol), I won't know if I answered the question about slope intercept form correctly because I won't have any examples explaining this to me! Does anyone have an easy, fool-proof way of remembering this and actually understanding it?! Thx sooo much.
Button navigates to signup pageComment on Saule 🍄✨💜's post “So here's my issue: I ans...”
(2 votes)
Answer
- Kim Seidel
  Posted 3 years ago. Direct link to Kim Seidel's post “Many processes in math ta...”
  Many processes in math take practice, practice and more practice. The more you practice, the less you need to have examples to look at.
  Comment on Kim Seidel's post “Many processes in math ta...”
  (2 votes)
Shams
Posted 6 months ago. Direct link to Shams's post “What if the y-intercept i...”
What if the y-intercept is 0? What happens then?
Button navigates to signup pageButton navigates to signup page
(2 votes)
Answer
- Kim Seidel
  Posted 6 months ago. Direct link to Kim Seidel's post “Then the equation becomes...”
  Then the equation becomes: y=mx
  since "b" is 0, it is not shown.
  Button navigates to signup page
  (2 votes)