If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Lesson 7: Writing slope-intercept equations

# Slope-intercept equation from slope & point

Learn how to write an equation in slope-intercept form (y=mx+b) for the line with a slope of -3/4 that goes through the point (0,8). We identify the slope (m) and y-intercept (b) to create our equation y = (-3/4)*x + 8. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• i fully understand that y=mx+b works when you are tryig to find out the y
but i do not understand why you have to +b
can someone please tell me why is that?
• b is your y-axis location and mx is to go up by x and go right by x
• I made my own equation:

(2,3) & (6,9)

thus:
9-3/6-2= 6/4 OR 1.5

Which equaled y=1.5x + b

I used 2-3 to make it
3=1.5(2)+b 3 being y 1.5 being M and (2) being X
which makes > 3=3+b

now when i put 3 on both sides of my equation, both 3's cancel out. Does this make b=0 OR do i have to use (6,9) instead of (2,3) OR is there no b?

~Callum :-)
• It's just a line which passes from origin. Try graphing it. You can use any point in the line, yet the b is always 0 since the line passes from origin. It's just a coincidence that the line passes from origin. The y intercept is at the origin AKA 0,0.
• why is it that there's an y-int but not a x-int??
• Most lines have both. It just happens that the slope-intercept form of the equation tells you the y-intercept. You can always calculate the x-intercept.
• When slope is 4 is it actually 4/1?
• 4 is the same as 4/1. Slope is some number of change in y per change in x, so a slope of 4 is the same as 4 units of change in y per one unit of change in x. Since 4/1 = 4, we say that the slope is 4. That is, the rate of change is 4. Does that make sense? Does that answer the question? I hope I was helpful!
• I thought that the slope was canceled out because of the zero, which changed the equation to y=b? I understand that the zero cancels itself out when multiplied but I dont understand why the "mx" came back after being canceled. Help me please
• the 'mx' only got canceled when we assumed the value of x=0 but as we move along the line the value of 'x' changes hence, mx comes back.
What I mean is
We know, y = mx + b
If x = 0, y=b, but since value of x may change we write the equation back in standard form
y=mx + b
• This is more of an order of operations question than anything else, but can someone explain to me "why" it would be improper to isolate the b and then make it positive before doing anything else? Please don't just say you wont get the correct answer if you don't do it correctly, I want you to explain how this is violating the order of operations and other cross equation simplifications are not violating those principles...

This is a screenshot of what the program says is the proper sequence:

This is a picture of the sequencing I'm confused about being wrong:

• In this step:
-b = (-13/6) (13) + 26,
b = (13/6) (-13) - 26
you've made a mistake. You distributed a negative to both m and x when they should get only a single negative between them. Essentially, you're saying that

-z = xy is the same as z = (-x)(-y), which is only true when z = 0.

Distributing the negative properly gives you
b = (13/6) (13) - 26 = 169/6 - 174/6 = -5/6,
as expected.
• remember that there's people who commented here that are now fully grown up
• my teacher can't teach :( can someone explain this a little better?
• What exactly are you confused about? People can help if you're specific with your questions.
• I have to write an equation in Slope intercept form y=mx+b
I have a slope of 3 and an x intercept of 2.
How do I solve that without a y intercept/
• The 1st response you received is incorrect. This is doable.
As you have already notices, we don't have the y-intercept. So, we need to calculate it. Remember, "b" in the form: "y=mx+b" is the y-intercept. We're going to use this formula and calculate "b". We have a value we can use for all the other variables: y = 0 (from x-intercept); x = 2 (from x-intercept) and m = 3. Substitute and calculate "b".
`0 = 3(2) + b`
`0 = 6 + b`
`-6 = b`

Now, we can create the equation of the line using slope of 3 and y-intercept of -6
`y = 3x - 6`
Hope this helps.