In the point slopes form, it looks like you're saying you could use either set of coordinates.I thought it was the first set of coordinates since it says x1 and y1. Please explain. Thanks.

That is correct. You can definitely use either set of coordinates. Don't mix-and-match: you can't use x1 and y2, but you can use (x1, y1) or (x2, y2) and it will work just as well either way.

How do you know when to use point slope form vs slope intercept form?

Most of the time, it would be your choice. Though, your teacher may request that you use a specific approach to see if you know how to do it.

when do you need to use slope?

To determining the slope/ steepness of a line. You should review the slope videos if you need help.

ax + by + c = 0 ax + by = c I've heard of 2 "standard" forms of linear equations. Which one is correct? should c in the 1st line be -c though? since im moving it from the right to left...?

hey! okay, so I'm pretty sure you're confusing a quadratic equation with a linear equation. A linear equation is a straight line, while a quadratic is a curve/parabola. You'll probably learn that later in algebra 1 and 2. anyways, the standard linear equation is ax+by=c, while the standard quadratic equation is slightly different from what you have; it should be ax^2+bx+c=0 hope this helps!!

Why are point-slope operations the opposite? For example, the point is (2,-3). why is y+3=3/4(x-2) correct but not y-3=3/4(x+2)?

Point slope form is a variation of the slope formula: Slope m = (y2-y1)/(x2-x1) If you mulitply both sides by (x2-x1), then you get point slope form: (y2-y1) = m(x2-x1) Then, they swab a couple of variables to clarify the variables that stay. X2 becomes X, and Y2 becomes Y. And, you have the point slope form. Remember, slope is calculated as the change in Y over the change in X. So, it requires the subtraction. Hope this helps.

what’s point-slope form going to be useful for?

Point slope form is important because it can give us another set of coordinate pairs when we are only given one. Using algebraic manipulation, you can find coordinates _and_ the slope from just that equation which helps with graphing. Being able to readily switch from different linear equation forms helps solving complex problems. Hope this helps. 🙃

at the end it says this is a standard form y+3x=−10 it sould be fist 3x +y= -10 isn't ?

Specifically there are a lot of teachers that would mark y+3x=−10 wrong. Maybe correctly; the form is the whole point of the exercise.

What happens when you have these coordinates (2,7) (6,7) and my slope ends up with 0/4, is this possible?

Yes! It is possible! if you end up with a slope of 0 or a fraction with zero as the numerator, that's known as a zero slope. On a graph, it looks like a horizontal line. Hope this helps!

Main content

Algebra 1

Course: Algebra 1 > Unit 5

Lesson 6: Summary: Forms of two-variable linear equations

Forms of linear equations review

CCSS.Math:

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.

There are three main forms of linear equations.

Slope-intercept	Point-slope	Standard
y, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #1fab54, b, end color #1fab54	y, minus, start color #7854ab, y, start subscript, 1, end subscript, end color #7854ab, equals, start color #ed5fa6, m, end color #ed5fa6, left parenthesis, x, minus, start color #7854ab, x, start subscript, 1, end subscript, end color #7854ab, right parenthesis	A, x, plus, B, y, equals, C
where start color #ed5fa6, m, end color #ed5fa6 is slope and start color #1fab54, b, end color #1fab54 is the y-intercept	where start color #ed5fa6, m, end color #ed5fa6 is slope and start color #7854ab, left parenthesis, x, start subscript, 1, end subscript, comma, y, start subscript, 1, end subscript, right parenthesis, end color #7854ab is a point on the line	where A, B, and C are constants

Example

A line passes through the points left parenthesis, minus, 2, comma, minus, 4, right parenthesis and left parenthesis, minus, 5, comma, 5, right parenthesis. Find the equation of the line in all three forms listed above.

Two of the forms require slope, so let's find that first.

\begin{aligned} \text{slope}=\maroonC m &= \dfrac{\Delta y}{\Delta x}\\\\ &=\dfrac{5-(-4)}{-5-(-2)}\\\\ &=\dfrac{9}{-3} \\\\ &=\maroonC{-3} \end{aligned}

Now we can plug in start color #ed5fa6, m, end color #ed5fa6 and one of the points, say start color #7854ab, left parenthesis, minus, 5, comma, 5, right parenthesis, end color #7854ab, to get point-slope form, y, minus, start color #7854ab, y, start subscript, 1, end subscript, end color #7854ab, equals, start color #ed5fa6, m, end color #ed5fa6, left parenthesis, x, minus, start color #7854ab, x, start subscript, 1, end subscript, end color #7854ab, right parenthesis:

\begin{aligned} y-\purpleD{y_1}&=\maroonC m(x-\purpleD{x_1}) \\\\ y-\purpleD{5}&=\maroonC{-3}(x-\purpleD{(-5)}) \\\\ y-\purpleD{5}&=\maroonC{-3}(x+\purpleD{5}) \end{aligned}

Solving for y, we get slope-intercept form, y, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #1fab54, b, end color #1fab54:

\begin{aligned} y-{5}&=\maroonC{-3}(x+{5}) \\\\ y-5&=\maroonC{-3}x-15 \\\\ y&=\maroonC{-3}x\greenD{-10} \end{aligned}

And adding 3, x to both sides, we get standard form, A, x, plus, B, y, equals, C:

y, plus, 3, x, equals, minus, 10

Want another example? Check out this video.

Want to practice the different forms yourself? Check out this exercise.

Want a more in-depth review of each form? Check out these review articles:

Want to join the conversation?

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Kelsen Miener
Posted 6 years ago. Direct link to Kelsen Miener's post “In the point slopes form,...”
In the point slopes form, it looks like you're saying you could use either set of coordinates.I thought it was the first set of coordinates since it says x1 and y1. Please explain. Thanks.
Button navigates to signup pageComment on Kelsen Miener's post “In the point slopes form,...”
(14 votes)
Answer
- Scott Ferguson
  Posted 3 years ago. Direct link to Scott Ferguson's post “That is correct. You can ...”
  That is correct. You can definitely use either set of coordinates. Don't mix-and-match: you can't use x1 and y2, but you can use (x1, y1) or (x2, y2) and it will work just as well either way.
  Button navigates to signup page
  (26 votes)
Betsy Glad
Posted 2 years ago. Direct link to Betsy Glad's post “How do you know when to u...”
How do you know when to use point slope form vs slope intercept form?
Button navigates to signup pageComment on Betsy Glad's post “How do you know when to u...”
(11 votes)
Answer
- Kim Seidel
  Posted 2 years ago. Direct link to Kim Seidel's post “Most of the time, it woul...”
  Most of the time, it would be your choice. Though, your teacher may request that you use a specific approach to see if you know how to do it.
  Button navigates to signup page
  (13 votes)
victoria.reed
Posted 6 years ago. Direct link to victoria.reed's post “when do you need to use s...”
when do you need to use slope?
Button navigates to signup pageComment on victoria.reed's post “when do you need to use s...”
(11 votes)
Answer
- James Gallagher
  Posted 4 months ago. Direct link to James Gallagher's post “To determining the slope/...”
  To determining the slope/ steepness of a line. You should review the slope videos if you need help.
  Button navigates to signup page
  (2 votes)
ZetaFox
Posted 2 years ago. Direct link to ZetaFox's post “ax + by + c = 0 ax + by =...”
ax + by + c = 0
ax + by = c

I've heard of 2 "standard" forms of linear equations. Which one is correct?

should c in the 1st line be -c though? since im moving it from the right to left...?
Button navigates to signup pageButton navigates to signup page
(6 votes)
Answer
- Khushi Viramgami
  Posted 2 years ago. Direct link to Khushi Viramgami's post “hey! okay, so I'm pretty ...”
  hey! okay, so I'm pretty sure you're confusing a quadratic equation with a linear equation. A linear equation is a straight line, while a quadratic is a curve/parabola. You'll probably learn that later in algebra 1 and 2.
  
  anyways, the standard linear equation is ax+by=c, while the standard quadratic equation is slightly different from what you have; it should be ax^2+bx+c=0
  
  hope this helps!!
  Comment on Khushi Viramgami's post “hey! okay, so I'm pretty ...”
  (12 votes)
em
Posted 3 years ago. Direct link to em's post “Why are point-slope opera...”
Why are point-slope operations the opposite?
For example, the point is (2,-3).
why is y+3=3/4(x-2) correct but not y-3=3/4(x+2)?
Button navigates to signup pageComment on em's post “Why are point-slope opera...”
(4 votes)
Answer
- Kim Seidel
  Posted 3 years ago. Direct link to Kim Seidel's post “Point slope form is a var...”
  Point slope form is a variation of the slope formula:
  Slope m = (y2-y1)/(x2-x1)
  If you mulitply both sides by (x2-x1), then you get point slope form:
  (y2-y1) = m(x2-x1)
  Then, they swab a couple of variables to clarify the variables that stay. X2 becomes X, and Y2 becomes Y. And, you have the point slope form.
  
  Remember, slope is calculated as the change in Y over the change in X. So, it requires the subtraction.
  
  Hope this helps.
  Button navigates to signup page
  (7 votes)
Corey Zuk
Posted 2 years ago. Direct link to Corey Zuk's post “i must be behind in math ...”
i must be behind in math because all of this is way too confusing
Button navigates to signup pageComment on Corey Zuk's post “i must be behind in math ...”
(7 votes)
Answer
ultraidiotboy
Posted 2 years ago. Direct link to ultraidiotboy's post “what’s point-slope form g...”
what’s point-slope form going to be useful for?
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- etoile~
  Posted 2 years ago. Direct link to etoile~'s post “Point slope form is impor...”
  Point slope form is important because it can give us another set of coordinate pairs when we are only given one. Using algebraic manipulation, you can find coordinates and the slope from just that equation which helps with graphing. Being able to readily switch from different linear equation forms helps solving complex problems. Hope this helps. 🙃
  Comment on etoile~'s post “Point slope form is impor...”
  (6 votes)
Stelios Kourentzis
Posted 3 years ago. Direct link to Stelios Kourentzis's post “at the end it says this i...”
at the end it says this is a standard form y+3x=−10
it sould be fist 3x +y= -10 isn't ?
Button navigates to signup pageButton navigates to signup page
(4 votes)
Answer
- Peter Dresslar
  Posted 2 years ago. Direct link to Peter Dresslar's post “Specifically there are a ...”
  Specifically there are a lot of teachers that would mark y+3x=−10 wrong. Maybe correctly; the form is the whole point of the exercise.
  Button navigates to signup page
  (2 votes)
worldsage
Posted 6 years ago. Direct link to worldsage's post “Is it possible to convert...”
Is it possible to convert standard form back to point-slope directly?
Button navigates to signup pageComment on worldsage's post “Is it possible to convert...”
(4 votes)
Answer
arlenecharles81
Posted 2 years ago. Direct link to arlenecharles81's post “What happens when you hav...”
What happens when you have these coordinates (2,7) (6,7) and my slope ends up with 0/4, is this possible?
Button navigates to signup pageButton navigates to signup page
(3 votes)
Answer
- Niquee A.
  Posted 2 years ago. Direct link to Niquee A.'s post “Yes! It is possible! if y...”
  Yes! It is possible! if you end up with a slope of 0 or a fraction with zero as the numerator, that's known as a zero slope. On a graph, it looks like a horizontal line. Hope this helps!
  Button navigates to signup page
  (5 votes)