In school I learned it as y-y1=m(x-x1). Is it this just another way to write the same thing? Thank you

Yes, it is essentially the same. Sal is just using the variables "a" and "b" instead of X1 and Y1.

what is the slope of the line through (1,0) and (3,8)?

Let's use the *slope formula*, where the slope (m) is equal to rise over run: m = rise / run = (y₂ - y₁) / (x₂ - x₁) = (8 - 0) / (3 - 1) = 8 / 2 = 4 m = 4, so the slope of the line through (1, 0) and (3, 8) is *4*. Hope this helps!

I understand how this can create an equation, but not how it could be solved to an answer with two unknowns. If it can't be solved, what is the purpose exactly? Thanks, Lilly

Linear equations are equations that when graphed create a line. Every point on the line is a solution to the equation. Before learning how to create the equation, you should have learned about how to find solutions and graph the equation. Try reviewing the lessons are: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs Hope this helps.

What does it mean when the slope is simply - and you are trying to graph an equation?

When the slope is . you should have to find it. You want to set up the problem like this: (-1,3) (-2,5) y-3=2(x-1) (answer) The 3 represents the y axis, and the -1 represents the x axis. you can interchange with the 2nd coordinate point. The 2 represents the slope. You can find the slope with slope-intercept form. Hope this helped.

how do you get that answer for number 2

What do you mean for number 2? I guess I'll just explain both problems here. Write the point-slope equation of the line that passes through (7,3) whose slope is 2. This is pretty straightforward, since point-slope form requires you to just substitute values in order to form the equation. Answer: y - 3 = 2(x - 7) Write the point-slope equation of the line that passes through (3,5) and (7,1). To solve this, you need to find the slope first. Slope for line connecting (x1, y1) and (x2, y2) is (y1 - y2) / (x1 - x2). Answer: y - 5 = -(x - 3) or y - 1 = -(x - 7) What is the slope of the line y - 5 = -4(x - 8)? Since both coefficient for both x and y are 1, you don't have to consider anything complicated. To know which point does the line pass through, just substitute for x and y and compare L.H.S. with R.H.S. Answer: -4 (8, 5) Graph y - 7 = -3(x - 1) There are many ways to do this, such as setting a point and doing some calculation but I will use another way. Recall slope is equal to *change of y-coordinate for every one unit change in the x-coordinate*. So if the slope is -3, it means for every 1 unit increase in x-coordinate, y-coordinate will reduce by 3 unit (-3). So we just take the point provided in the equation (1, 7) and take another point (1 + 1, 7 - 3) = (2, 4)

What is the slope of a line that passes through the points (1,3)(1,3)left parenthesis, 1, comma, 3, right parenthesis and (7,5)(7,5)left parenthesis, 7, comma, 5, right parenthesis in the xyxyx, y-plane?

Your post is unreadable in its current form. It looks like you need to find the slope and you have 2 points. 1) Label one point as (x1, y1) and the other point as (x2,y2) 2) Then use the slope formula: m = (y2-y1)/(x2-x1). Take each values from your points and put them into the corresponding variable in the formula. 3) Then, do the math to simplify the fraction. The result will be your slope.

Main content

Algebra 1

Course: Algebra 1 > Unit 5

Lesson 4: Point-slope form

Point-slope form review

Google Classroom

Review point-slope form and how to use it to solve problems.

What is point-slope form?

Point-slope is a specific form of linear equations in two variables:

y, minus, start color #1fab54, b, end color #1fab54, equals, start color #ed5fa6, m, end color #ed5fa6, left parenthesis, x, minus, start color #11accd, a, end color #11accd, right parenthesis

When an equation is written in this form, start color #ed5fa6, m, end color #ed5fa6 gives the slope of the line and left parenthesis, start color #11accd, a, end color #11accd, comma, start color #1fab54, b, end color #1fab54, right parenthesis is a point the line passes through.

This form is derived from the slope formula.

Want to learn more about point-slope form? Check out this video.

Finding point-slope equation from features or graph

Example 1: Equation from slope and point

Suppose we want to find the equation of the line that passes through left parenthesis, start color #11accd, 1, end color #11accd, comma, start color #1fab54, 5, end color #1fab54, right parenthesis and whose slope is start color #ed5fa6, minus, 2, end color #ed5fa6. Well, we simply plug start color #ed5fa6, m, equals, minus, 2, end color #ed5fa6, start color #11accd, a, equals, 1, end color #11accd, and start color #1fab54, b, equals, 5, end color #1fab54 into point-slope form!

y, minus, start color #1fab54, 5, end color #1fab54, equals, start color #ed5fa6, minus, 2, end color #ed5fa6, left parenthesis, x, minus, start color #11accd, 1, end color #11accd, right parenthesis

Example 2: Equation from two points

Suppose we want to find the line that passes through the points left parenthesis, 1, comma, 4, right parenthesis and left parenthesis, 6, comma, 19, right parenthesis. First, we use the two points to find the slope:

\begin{aligned} Slope & = \frac{19 - 4}{6 - 1} \\ = \frac{15}{5} \\ = 3 \end{aligned}

Now we use one of the points, let's take left parenthesis, start color #11accd, 1, end color #11accd, comma, start color #1fab54, 4, end color #1fab54, right parenthesis, and write the equation in point-slope:

y, minus, start color #1fab54, 4, end color #1fab54, equals, start color #ed5fa6, 3, end color #ed5fa6, left parenthesis, x, minus, start color #11accd, 1, end color #11accd, right parenthesis

Problem 1

Current

Write the point-slope equation of the line that passes through left parenthesis, 7, comma, 3, right parenthesis whose slope is 2.

Want to try more problems like this? Check out this exercise.

Finding features and graph from point-slope equation

When we have a linear equation in point-slope form, we can quickly find the slope of the corresponding line and a point it passes through. This also allows us to graph it.

Consider the equation y, minus, start color #1fab54, 1, end color #1fab54, equals, start color #ed5fa6, 2, end color #ed5fa6, left parenthesis, x, minus, start color #11accd, 3, end color #11accd, right parenthesis. We can tell that the corresponding line passes through left parenthesis, start color #11accd, 3, end color #11accd, comma, start color #1fab54, 1, end color #1fab54, right parenthesis and has a slope of start color #ed5fa6, 2, end color #ed5fa6. Now we can graph the line:

Problem 1

Current

What is the slope of the line y, minus, 5, equals, minus, 4, left parenthesis, x, minus, 8, right parenthesis?

The line passes through which point?

(Choice A)
left parenthesis, 5, comma, 8, right parenthesis
(Choice B)
left parenthesis, 8, comma, 5, right parenthesis
(Choice C)
left parenthesis, minus, 5, comma, minus, 8, right parenthesis
(Choice D)
left parenthesis, minus, 8, comma, minus, 5, right parenthesis

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Simmy :)
Posted 5 years ago. Direct link to Simmy :)'s post “In school I learned it as...”
In school I learned it as y-y1=m(x-x1). Is it this just another way to write the same thing? Thank you
Button navigates to signup pageButton navigates to signup page
(36 votes)
Answer
- Kim Seidel
  Posted 5 years ago. Direct link to Kim Seidel's post “Yes, it is essentially th...”
  Yes, it is essentially the same. Sal is just using the variables "a" and "b" instead of X1 and Y1.
  Comment on Kim Seidel's post “Yes, it is essentially th...”
  (34 votes)
Natia Island
Posted 4 years ago. Direct link to Natia Island's post “what is the slope of the ...”
what is the slope of the line through (1,0) and (3,8)?
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(8 votes)
Answer
- Polina Vitić
  Posted 4 years ago. Direct link to Polina Vitić's post “Let's use the *slope form...”
  Let's use the slope formula, where the slope (m) is equal to rise over run:
  
  m = rise / run
  = (y₂ - y₁) / (x₂ - x₁)
  = (8 - 0) / (3 - 1)
  = 8 / 2
  = 4
  
  m = 4, so the slope of the line through (1, 0) and (3, 8) is 4.
  
  Hope this helps!
  Button navigates to signup page
  (25 votes)
ogeise001
Posted 3 months ago. Direct link to ogeise001's post “how do you get that answe...”
how do you get that answer for number 2
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(4 votes)
Answer
- joshua
  Posted 3 months ago. Direct link to joshua's post “What do you mean for numb...”
  What do you mean for number 2? I guess I'll just explain both problems here.
  
  Write the point-slope equation of the line that passes through (7,3) whose slope is 2.
  
  This is pretty straightforward, since point-slope form requires you to just substitute values in order to form the equation.
  Answer: y - 3 = 2(x - 7)
  
  Write the point-slope equation of the line that passes through (3,5) and (7,1).
  
  To solve this, you need to find the slope first. Slope for line connecting (x1, y1) and (x2, y2) is
  (y1 - y2) / (x1 - x2).
  Answer: y - 5 = -(x - 3) or y - 1 = -(x - 7)
  
  What is the slope of the line y - 5 = -4(x - 8)?
  
  Since both coefficient for both x and y are 1, you don't have to consider anything complicated.
  
  To know which point does the line pass through, just substitute for x and y and compare L.H.S. with R.H.S.
  Answer: -4 (8, 5)
  
  Graph y - 7 = -3(x - 1)
  
  There are many ways to do this, such as setting a point and doing some calculation but I will use another way. Recall slope is equal to change of y-coordinate for every one unit change in the x-coordinate. So if the slope is -3, it means for every 1 unit increase in x-coordinate, y-coordinate will reduce by 3 unit (-3). So we just take the point provided in the equation (1, 7) and take another point (1 + 1, 7 - 3) = (2, 4)
  Comment on joshua's post “What do you mean for numb...”
  (19 votes)
crzy4excellence
Posted 5 months ago. Direct link to crzy4excellence's post “So this is why my dad dro...”
So this is why my dad dropped out of 9th grade. LOL
Button navigates to signup pageComment on crzy4excellence's post “So this is why my dad dro...”
(12 votes)
Answer
hannah.mcgregor
Posted 4 years ago. Direct link to hannah.mcgregor's post “I understand how this can...”
I understand how this can create an equation, but not how it could be solved to an answer with two unknowns. If it can't be solved, what is the purpose exactly?
Thanks, Lilly
Button navigates to signup pageComment on hannah.mcgregor's post “I understand how this can...”
(5 votes)
Answer
- Kim Seidel
  Posted 4 years ago. Direct link to Kim Seidel's post “Linear equations are equa...”
  Linear equations are equations that when graphed create a line.
  Every point on the line is a solution to the equation. Before learning how to create the equation, you should have learned about how to find solutions and graph the equation. Try reviewing the lessons are: https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs
  
  Hope this helps.
  Button navigates to signup page
  (9 votes)
taisiya Matev
Posted 6 years ago. Direct link to taisiya Matev's post “What does it mean when th...”
What does it mean when the slope is simply - and you are trying to graph an equation?
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(5 votes)
Answer
- Jacob Beauvais
  Posted 6 years ago. Direct link to Jacob Beauvais's post “When the slope is . you s...”
  When the slope is . you should have to find it. You want to set up the problem like this:
  (-1,3) (-2,5)
  y-3=2(x-1) (answer)
  The 3 represents the y axis, and the -1 represents the x axis. you can interchange with the 2nd coordinate point. The 2 represents the slope. You can find the slope with slope-intercept form. Hope this helped.
  Comment on Jacob Beauvais's post “When the slope is . you s...”
  (7 votes)
Violeta 😾
Posted 3 years ago. Direct link to Violeta 😾's post “Im confused on how to fin...”
Im confused on how to find slope. any tips anyone?
Button navigates to signup pageComment on Violeta 😾's post “Im confused on how to fin...”
(4 votes)
Answer
- Ashur Hamilton
  Posted 2 years ago. Direct link to Ashur Hamilton's post “change in y / change in x”
  change in y / change in x
  Button navigates to signup page
  (4 votes)
bollesa
Posted 9 months ago. Direct link to bollesa's post “So this is basically (cha...”
So this is basically (change in y)=(slope)(change in x)?
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(3 votes)
Answer
- Kim Seidel
  Posted 9 months ago. Direct link to Kim Seidel's post “Yes, good observation.”
  Yes, good observation.
  Button navigates to signup page
  (5 votes)
mcdonand001
Posted 20 days ago. Direct link to mcdonand001's post “What is the slope of a li...”
What is the slope of a line that passes through the points (1,3)(1,3)left parenthesis, 1, comma, 3, right parenthesis and (7,5)(7,5)left parenthesis, 7, comma, 5, right parenthesis in the xyxyx, y-plane?
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(4 votes)
Answer
- Kim Seidel
  Posted 20 days ago. Direct link to Kim Seidel's post “Your post is unreadable i...”
  Your post is unreadable in its current form. It looks like you need to find the slope and you have 2 points.
  1) Label one point as (x1, y1) and the other point as (x2,y2)
  2) Then use the slope formula: m = (y2-y1)/(x2-x1). Take each values from your points and put them into the corresponding variable in the formula.
  3) Then, do the math to simplify the fraction. The result will be your slope.
  Button navigates to signup page
  (2 votes)
ss1309996
Posted 3 years ago. Direct link to ss1309996's post “One line passes through t...”
One line passes through the points \blueD{(-8,1)}(−8,1)start color #11accd, left parenthesis, minus, 8, comma, 1, right parenthesis, end color #11accd and \blueD{(4,4)}(4,4)start color #11accd, left parenthesis, 4, comma, 4, right parenthesis, end color #11accd. Another line passes through points \greenD{(-9,-7)}(−9,−7)start color #1fab54, left parenthesis, minus, 9, comma, minus, 7, right parenthesis, end color #1fab54 and \greenD{(9,-3)}(9,−3)start color #1fab54, left parenthesis, 9, comma, minus, 3, right parenthesis, end color #1fab54.
Are the lines parallel, perpendicular, or neither
Button navigates to signup pageComment on ss1309996's post “One line passes through t...”
(4 votes)
Answer