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### Course: Get ready for AP® Calculus > Unit 2

Lesson 2: 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?(110 votes)- b is your y-axis location and mx is to go up by x and go right by x(8 votes)

- 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 :-)(27 votes)- 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.(8 votes)

- why is it that there's an y-int but not a x-int??(18 votes)
- 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.(14 votes)

- When slope is 4 is it actually 4/1?(12 votes)
- 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!(15 votes)

- 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(9 votes)
- 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(12 votes)

- remember that there's people who commented here that are now fully grown up(9 votes)
- 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:

https://drive.google.com/file/d/0B0a8mT2yOILSRTNkNkJESEpDZDg/view?usp=sharing

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

https://drive.google.com/file/d/0B0a8mT2yOILSdkEzdEhqbjBncE0/view?usp=sharing(6 votes)- 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.(6 votes)

- my teacher can't teach :( can someone explain this a little better?(7 votes)
- What exactly are you confused about? People can help if you're specific with your questions.(1 vote)

- 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/(4 votes)- 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.(8 votes)

- How come when you use a different coordinate to find b I am getting a different answer?(5 votes)
- Any point on the line with the slope can be used to find the value of "b". It is always the same number. If you got a different result using a different point, then you have a math error. Without a specific example and your work, i can't tell what you did wrong.(2 votes)

## Video transcript

A line has a slope of negative
3/4 and goes through the point 0 comma 8. What is the equation of this
line in slope-intercept form? So any line can be represented
in slope-intercept form, is y is equal to mx plus b,
where this m right over here, that is of the
slope of the line. And this b over here, this is
the y-intercept of the line. Let me draw a quick
line here just so that we can visualize
that a little bit. So that is my y-axis. And then that is my x-axis. And let me draw a line. And since our line here
has a negative slope, I'll draw a downward
sloping line. So let's say our line
looks something like that. So hopefully, we're a little
familiar with the slope already. The slope essentially
tells us, look, start at some point
on the line, and go to some other point
of the line, measure how much you had to move in the
x direction, that is your run, and then measure
how much you had to move in the y direction,
that is your rise. And our slope is equal
to rise over run. And you can see over here,
we'd be downward sloping. Because if you move in
the positive x direction, we have to go down. If our run is positive,
our rise here is negative. So this would be a
negative over a positive, it would give you
a negative number. That makes sense, because
we're downward sloping. The more we go down
in this situation, for every step we
move to the right, the more downward
sloping will be, the more of a negative
slope we'll have. So that's slope right over here. The y-intercept just tells us
where we intercept the y-axis. So the y-intercept, this
point right over here, this is where the line
intersects with the y-axis. This will be the
point 0 comma b. And this actually just falls
straight out of this equation. When x is equal to
0-- so let's evaluate this equation, when
x is equal to 0. y will be equal to
m times 0 plus b. Well, anything times 0 is 0. So y is equal to 0
plus b, or y will be equal to b, when
x is equal to 0. So this is the point 0 comma b. Now, they tell us what
the slope of this line is. They tell us a line has
a slope of negative 3/4. So we know that our
slope is negative 3/4, and they tell us that the
line goes through the point 0 comma 8. They tell us we go through the--
Let me just, in a new color. I've already used orange,
let me use this green color. They tell us what we go
through the point 0 comma 8. Notice, x is 0. So we're on the y-axis. When x is 0, we're
on the y-axis. So this is our y-intercept. So b, we could say-- we could
do a couple-- our y-intercept is the point 0 comma 8, or we
could say that b-- Remember, it's also 0 comma b. We could say b is equal to 8. So we know m is equal to
negative 3/4, b is equal to 8, so we can write the
equation of this line in slope-intercept form. It's y is equal to negative
3/4 times x plus b, plus 8. And we are done.