I think I may need to give up and be a farmer because this is to hard

Alexis, I am in my 40's relearning this. Don't give up. Plus, farmers use TONs (TONNES, depending on where you live) of maths. Keep practicing, every wrong answer is still learning.

everything about what we are learning I don't understand

You may need to go back to wherever you feel comfortable with, and learn upward again slowly. You can do this within Khan Academy.

i think i'll just sell corn on the street

fr but i think lemonade would be better

On number 4, why would b=17?

This is the process they show you: y =−4x+b 9 =−4⋅2+b 9 =−8+b 17=b ---------- In THIS ("9 =−8+b") step they are subtracting -8 from 9 which looks like this: 9-(-8). We know that two negative operations make a positive sum, which is why the answer is 17 : 9-(-8) = 17.

What is the rule with deciding which point value gets subtracted from the other?

It doesn't matter. The only difference is that there's a sign change, but since this happens both for 𝛥𝑦 as for 𝛥𝑥 these changes cancel out when we divide the two (𝛥𝑦∕𝛥𝑥). 𝛥𝑦 = 𝑦₂ − 𝑦₁ = −(𝑦₁ − 𝑦₂) 𝛥𝑥 = 𝑥₂ − 𝑥₁ = −(𝑥₁ − 𝑥₂) ⇒ 𝛥𝑦∕𝛥𝑥 = (𝑦₂ − 𝑦₁)∕(𝑥₂ − 𝑥₁) = −(𝑦₁ − 𝑦₂)∕(−(𝑥₁ − 𝑥₂)) = (𝑦₁ − 𝑦₂)∕(𝑥₁ − 𝑥₂)

how do you change 7x+3y=3 into slope intercept form

For something to be in slope-intercept for, y needs to be isolated on one side of the equation. Here's how you'd do that: ```7x + 3y = 3``` Subtract 7x from both sides: ```7x + 3y - 7x = 3 - 7x``` Simplify: ```3y = 3 - 7x``` Now, divide both sides by 3: ```3y/3 = 3/3 - 7x/3``` Simplify: ```y = 1 - (7/3)x``` Usually, we have the intercept (in this case 1) on the right side, so simply move it: ```y = -(7/3)x + 1```

Main content

Algebra 1

Course: Algebra 1 > Unit 5

Lesson 3: Writing slope-intercept equations

Writing slope-intercept equations

CCSS.Math:

Learn how to find the slope-intercept equation of a line from two points on that line.

If you haven't read it yet, you might want to start with our introduction to slope-intercept form.

Writing equations from y-intercept and another point

Let's write the equation of the line that passes through the points left parenthesis, 0, comma, 3, right parenthesis and left parenthesis, 2, comma, 7, right parenthesis in slope-intercept form.

Recall that in the general slope-intercept equation y, equals, start color #ed5fa6, m, end color #ed5fa6, x, plus, start color #0d923f, b, end color #0d923f, the slope is given by start color #ed5fa6, m, end color #ed5fa6 and the y-intercept is given by start color #0d923f, b, end color #0d923f.

Finding start color #0d923f, b, end color #0d923f

The y-intercept of the line is left parenthesis, 0, comma, start color #0d923f, 3, end color #0d923f, right parenthesis, so we know that start color #0d923f, b, end color #0d923f, equals, start color #0d923f, 3, end color #0d923f.

Finding start color #ed5fa6, m, end color #ed5fa6

Recall that the slope of a line 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

Therefore, this is the slope between the points left parenthesis, 0, comma, 3, right parenthesis and left parenthesis, 2, comma, 7, right parenthesis:

\begin{aligned}\maroonC{m}&=\dfrac{\text{Change in }y}{\text{Change in }x} \\\\ &=\dfrac{7-3}{2-0} \\\\ &=\dfrac{4}{2} \\\\ &=\maroonC{2}\end{aligned}

In conclusion, the equation of the line is y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, start color #0d923f, plus, 3, end color #0d923f.

Check your understanding

Problem 1

Write the equation of the line.

Problem 2

Write the equation of the line.

Writing equations from any two points

Let's write the equation of the line that passes through left parenthesis, 2, comma, 5, right parenthesis and left parenthesis, 4, comma, 9, right parenthesis in slope-intercept form.

Note that we are not given the y-intercept of the line. This makes things a little bit more difficult, but we are not afraid of a challenge!

Finding start color #ed5fa6, m, end color #ed5fa6

\begin{aligned} \maroonC{m}&=\dfrac{\text{Change in }y}{\text{Change in }x} \\\\ &=\dfrac{9-5}{4-2} \\\\ &=\dfrac{4}{2} \\\\ &=\maroonC{2} \end{aligned}

Finding start color #0d923f, b, end color #0d923f

We know that the line is of the form y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, plus, start color #0d923f, b, end color #0d923f, but we still need to find start color #0d923f, b, end color #0d923f. To do that, we substitute the point left parenthesis, 2, comma, 5, right parenthesis into the equation.

Because any point on a line must satisfy that line’s equation, we get an equation that we can solve to find start color #0d923f, b, end color #0d923f.

[I need more explanation on this step.]

\begin{aligned}y&=\maroonC{2}\cdot x+\greenE{b}\\\\ 5&=\maroonC{2}\cdot 2+\greenE{b}&\gray{x=2\text{ and }y=5}\\\\ 5&=4+\greenE{b}\\\\ \greenE{1}&=\greenE{b} \end{aligned}

In conclusion, the equation of the line is y, equals, start color #ed5fa6, 2, end color #ed5fa6, x, start color #0d923f, plus, 1, end color #0d923f.

Check your understanding

Problem 3

Write the equation of the line.

Problem 4

Write the equation of the line.

Challenge problem

A line passes through the points left parenthesis, 5, comma, 35, right parenthesis and left parenthesis, 9, comma, 55, right parenthesis.

Write the equation of the line.

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Alexis
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I think I may need to give up and be a farmer because this is to hard
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- pdinthekr
  Posted 2 years ago. Direct link to pdinthekr's post “Alexis, I am in my 40's r...”
  Alexis, I am in my 40's relearning this. Don't give up. Plus, farmers use TONs (TONNES, depending on where you live) of maths. Keep practicing, every wrong answer is still learning.
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everything about what we are learning I don't understand
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- Thien D Ho
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  You may need to go back to wherever you feel comfortable with, and learn upward again slowly. You can do this within Khan Academy.
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ahernandez26
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i think i'll just sell corn on the street
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  fr but i think lemonade would be better
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crosshillary
Posted 5 years ago. Direct link to crosshillary's post “What is the rule with dec...”
What is the rule with deciding which point value gets subtracted from the other?
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(17 votes)
Answer
- Jerry Nilsson
  Posted 5 years ago. Direct link to Jerry Nilsson's post “It doesn't matter. The on...”
  It doesn't matter. The only difference is that there's a sign change, but since this happens both for 𝛥𝑦 as for 𝛥𝑥 these changes cancel out when we divide the two (𝛥𝑦∕𝛥𝑥).
  
  𝛥𝑦 = 𝑦₂ − 𝑦₁ = −(𝑦₁ − 𝑦₂)
  𝛥𝑥 = 𝑥₂ − 𝑥₁ = −(𝑥₁ − 𝑥₂)
  ⇒
  𝛥𝑦∕𝛥𝑥 = (𝑦₂ − 𝑦₁)∕(𝑥₂ − 𝑥₁) = −(𝑦₁ − 𝑦₂)∕(−(𝑥₁ − 𝑥₂)) = (𝑦₁ − 𝑦₂)∕(𝑥₁ − 𝑥₂)
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Anna
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On number 4, why would b=17?
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- Diya
  Posted 4 years ago. Direct link to Diya's post “This is the process they ...”
  This is the process they show you:
  y =−4x+b
  9 =−4⋅2+b
  9 =−8+b
  17=b
  ----------
  In THIS ("9 =−8+b") step they are subtracting -8 from 9 which looks like this: 9-(-8). We know that two negative operations make a positive sum, which is why the answer is 17 : 9-(-8) = 17.
  
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Bruh this is hard to do. I still dont undertand
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no way that this makes a single drop of sense
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how do you change 7x+3y=3 into slope intercept form
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- Admiral Betasin
  Posted 5 years ago. Direct link to Admiral Betasin's post “For something to be in sl...”
  For something to be in slope-intercept for, y needs to be isolated on one side of the equation.
  Here's how you'd do that:
  7x + 3y = 3
  
  Subtract 7x from both sides:
  7x + 3y - 7x = 3 - 7x
  
  Simplify:
  3y = 3 - 7x
  
  Now, divide both sides by 3:
  3y/3 = 3/3 - 7x/3
  
  Simplify:
  y = 1 - (7/3)x
  
  Usually, we have the intercept (in this case 1) on the right side, so simply move it:
  y = -(7/3)x + 1
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Math teacher who?! Khan Acadamy is so much better
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Answer

Algebra 1

Course: Algebra 1 > Unit 5

Writing equations from yyyy-intercept and another point

Finding b\greenE bbstart color #0d923f, b, end color #0d923f

Finding m\maroonC mmstart color #ed5fa6, m, end color #ed5fa6

Check your understanding

Writing equations from any two points

Finding m\maroonC mmstart color #ed5fa6, m, end color #ed5fa6

Finding b\greenE bbstart color #0d923f, b, end color #0d923f

Check your understanding

Want to join the conversation?

Writing equations from y-intercept and another point

Finding start color #0d923f, b, end color #0d923f

Finding start color #ed5fa6, m, end color #ed5fa6

Finding start color #ed5fa6, m, end color #ed5fa6

Finding start color #0d923f, b, end color #0d923f