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### Course: 8th grade (Illustrative Mathematics) > Unit 3

Lesson 4: Lesson 8: Translating to y=mx+b# Graph from slope-intercept equation

To graph a linear equation in slope-intercept form, we can use the information given by that form. For example, y=2x+3 tells us that the slope of the line is 2 and the y-intercept is at (0,3). This gives us one point the line goes through, and the direction we should continue from that point to draw the entire line. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

- What if the slope is a whole number like 3? Would it move 3 on the Y axis every time it's moved 1 on the X? (I know my terminology is probably off but you get the point)(74 votes)
- Yes, exactly! When you put 3 as a fraction it would be 3/1, right? Go up 3, and go right one.(31 votes)

- my mind is already fried, i cant do this lol(65 votes)
- i agree with that, very relatable(16 votes)

- After all of this i still don't get it(36 votes)
- Fr Khan academy is not my favorite source but my teachers have us use it.(15 votes)

- since your y intercept was a negative shouldn't the slope be a negative(2 votes)
- No, the y intercept has nothing to do with the slope.(31 votes)

- When will I use this in real life, not in a math classroom.(25 votes)
- After watching this video, I'm still confused. I wish there was a way to get a video on the questions I'm getting. For example: y=3x-3 or y=-x+1 or y=1/2x-2. I am visual, it would teach me much better. But whatever, I'll keep trying!(16 votes)
- Your examples work the same way as the video. The constant term will always be your y-intercept, and the coefficient of x will always be your slope. Once you plot your y-intercept, plot another point using your slope. Then connect the dots! If you want to make sure you got it correct, you can also plot an extra point, but you don't have to.(5 votes)

- How would you write 6x+5y=20 in plot-intercept form. I can't seem to figure out how you can divide 6x by 5.

The video is great. Thanks(7 votes)- So you're trying to put 6x+5y=20 into y=mx+b.

Let's try it step by step:

6x+5y=20

6x+5y(-6x)=20(-6x) --> 5y=20-6x

5y(/5)=20-6x (/5) --> y=4-6x/5 (whether you write it as 6x/5 or (6/5)x.. it doesn't really matter, because it's the same thing)

I hope that helps - I see where you are getting confused. That was also my problem when I was learning this...(16 votes)

- But in my question, I don't have a fraction and therefore don't know the slope. What do I do?(5 votes)
- If your equation is of the form: y=mx+b, then you do have a slope. The slope does not need to look like a fraction. For example:

y=2x-5. The slope=2. As a fraction this is 2/1.

y=x-5. The slope=1. As a fraction this is 1/1

y=0.5x-3. The slope=0.5, which in fraction form is 1/2

Hope this helps.(13 votes)

- trust my it is only asbad as u make it(3 votes)

- Would the change in Y over the change in X be the same as rise/run(rise over run) ? Rise being the the change in Y and run being the change in X. I learned it differently and wasn't sure if it was the same equation.(5 votes)
- They are the same. Both "change in Y over change in x" and "rise/run" are common phrases used to describe the slope.(5 votes)

## Video transcript

We are asked to graph y is
equal to 1/3x minus 2. Now, whenever you see an
equation in this form, this is called slope-intercept form. And the general way of writing
it is y is equal to mx plus b, where m is the slope. And here in this case, m is
equal to 1/3-- so let me write that down-- m is equal to 1/3,
and b is the y-intercept. So in this case, b is
equal to negative 2. And you know that b is the
y-intercept, because we know that the y-intercept occurs
when x is equal to 0. So if x is equal to 0 in either
of these situations, this term just becomes 0 and
y will be equal to b. So that's what we mean by
b is the y-intercept. So whenever you look at an
equation in this form, it's actually fairly straightforward to graph this line. b is the y-intercept. In this case it is negative 2,
so that means that this line must intersect the y-axis at y
is equal to negative 2, so it's this point right here. Negative 1, negative 2, this
is the point 0, negative 2. If you don't believe me, there's
nothing magical about this, try evaluating or
try solving for y when x is equal to 0. When x is equal to 0, this term
cancels out and you're just left with y is equal
to negative 2. So that's the y-intercept
right there. Now, this 1/3 tells us the
slope of the line. How much do we change in
y for any change in x? So this tells us that
1/3, so that right there, is the slope. So it tells us that 1/3 is equal
to the change in y over the change in x. Or another way to think about
it, if x changes by 3, then y would change by 1. So let me graph that. So we know that this point is
on the graph, that's the y-intercept. The slope tells us that if x
changes by 3-- so let me go 3 three to the right, 1, 2, 3--
that y will change by 1. So this must also be a
point on the graph. And we could keep doing that. If x changes by 3,
y changes by 1. If x goes down by 3, y
will go down by 1. If x goes down by 6, y
will go down by 2. It's that same ratio, so
1, 2, 3, 4, 5, 6, 1, 2. And you can see all of these
points are on the line, and the line is the graph of
this equation up here. So let me graph it. So it'll look something
like that. And you're done.